© The Author(s), Published by EDP Sciences, 2024

1 Introduction

With the accelerated construction of urban rail transit networks and high-class highways in recent years, traffic noise has become an important aspect that affects the life quality of people and ranks high on the list of most complained forms of pollution. In order to ease urban traffic pressure and protect ecological environment, underground metro transportation systems have been constructed worldwide. When metro trains pass through tunnels near buildings, the contact between wheels and rails generates waves that overlap with the waves produced by the train’s movement. Due to the tunnel structure, the vibration caused by these waves propagates to surrounding soil and subsequently reaches the foundations of buildings through soil. This vibration causes the structure and objects inside building to vibrate [1], resulting in secondary radiation noise [2]. With the continuous development of metro traffic system, the issue of secondary radiation noise caused by indoor vibration due to metro operation has become increasingly severe [3], leading to a significant rise in public complaint [4]. Accordingly, there is a need to explore effective strategies to reduce the negative impacts of secondary radiation noise.

Auditory masking, which relies on the decline in people’s ability to perceive one sound in the presence of another [5], has proven effective in mitigating the negative reaction due to original noise through the introduction of a new sound, and has been applied in various environments [6, 7]. A great number of studies based on auditory masking concentrated on proposing strategies for improving the reactions caused by road traffic noises [8–16], but given the differences in vehicle type, running speed and carrying capacity between underground metro and road vehicles and the fact that road traffic noise is an airborne noise while secondary radiation noise is a structural one, the acoustic features of the two can be very different. Since acoustic features such as spectral shape, loudness, tone, and timbre have been shown to influence subjective reactions [17–20], previous findings regarding the auditory masking of road traffic noise may not apply to secondary radiation noise. Therefore, it is crucial to discuss the impact of auditory masking on secondary radiation noise, an area of research that is still in its early stages and deserves further investigation.

When it comes to the types of masking sound, a great number of previous studies added natural sounds [21], modulated sounds [22], colored noises [23], and combined sounds [24] to unwanted sounds. Considering that secondary radiation noise was perceived mostly in indoor conditions, and the addition of water sound (a type of natural sound) was a commonly used method to optimize acoustic environment quality, the following descriptions primarily focused on indoor sound masking based on water sounds. Yang et al. conducted laboratory experiments to investigate the energetic masking potential of indoor water sounds in enhancing the perceptual quality amidst environmental noises infiltrating through windows. Their findings revealed that the introduction of water sounds significantly increased the perceived pleasantness, tranquility, and naturalness in the presence of environmental noise, while simultaneously decreasing the perception of noise, loudness, and annoyance associated with it [25]. Lam et al. discussed the perception due to active noise (traffic, train, and aircraft) after the addition of water sound in a model bedroom. They believed adding water sounds achieved the effects of energy masking and generally improved the overall acoustic comfort, while it seemed to lead to an increase of loudness [26]. Leung et al. conducted a series of laboratory experiments, which aimed to evaluate the masking effects of fountain sound and stream sound on annoyance level (energetic masking) due to road traffic noise on a busy trunk road, and the results showed that the addition of water sound reduced the annoyance level due to road traffic noise, with the stream sound showing a slightly stronger ability to improve annoyance than the fountain sound [12]. Wang et al. delved into the energetic masking mechanisms of four different water sounds—namely, fountain, stream, water-drop, and waterfall sounds—on the dissatisfaction triggered by secondary radiation noise within a high-rise building. The subjective survey results under a laboratory condition revealed that the optimization effect of water-drop sound was the best, followed by the fountain and stream sounds, and the waterfall sound was the least capable [27]. The effectiveness of certain water sounds as masking agents lies in the fact that the natural sounds of water create a distracting effect, diverting attention from unwanted noise. As a result, individuals’ reactions to original noises tend to improve as they become aware of and enjoy the pleasant water sounds. Furthermore, previous studies also indicated that the optimization effect was related to various acoustic characteristics of added water sound and original noise, including water sound type, spectral feature, sound pressure level (SPL), weighted signal-to-noise ratio (WSNR), among others. This means when analyzing the optimization mechanism, it is necessary to consider the influence of the above factors as much as possible. In addition, although Wang et al. compared four types of water sounds (fountain, stream, water-drop, and waterfall sounds) in terms of their ability to mitigate the dissatisfaction resulting from secondary radiation noise [27], relying solely on a single evaluation index, namely dissatisfaction, is insufficient to capture the diverse negative reactions that noise typically elicits, such as depression, annoyance, and discomfort [28]. Therefore, to obtain more accurate and comprehensive auditory masking analysis results, it is necessary to analyze the masking mechanisms of secondary radiation noise based on multiple types of subjective evaluation indexes.

To predict the effects of simultaneous exposure to two or more types of sounds on human reactions, a series of empirical models have been proposed. These include the energy summation model [29], the independent effects model [29], the energy difference model [29], the response-summation model [30], the summation and inhibition model [31], the annoyance equivalents model [32], and the dominant source model [33]. A large number of studies examined the abilities of these models to predict the reactions due to combined unwanted sounds. Marquis-Favre et al. evaluated the effectiveness of some empirical models for predicting the total annoyance induced by the combined road, railway and aircraft traffic noises. They suggested that the dominant source model (the total reaction level due to combined noise source is equal to the maximum reaction level caused by any single source) was the optimal model for assessing the total mean annoyance rating, and total annoyance could be better predicted based on the perceptual total annoyance models (linking total annoyance level to perceptual data, such as partial annoyance level) than the psychophysical total annoyance models (linking total annoyance level to one or several noise objective metrics) [34]. Pierrette et al. discussed the annoyance caused by the combination of industrial and road traffic noises and discovered that the strongest component model and a perceptual mixed model were the most suitable for calculating the total annoyance level [35]. Jeon et al. discovered that a quantification model, specifically a mathematical statistics model grounded in past experience, could effectively assess the overall dissatisfaction with indoor noises, encompassing floor impact, airborne, drainage, and traffic sounds. Besides, the results obtained from this quantification model exhibited strong correlation with those derived from the dominant source model and the energy equivalent model [36]. Several studies also examined the predictive powers of these models for the reaction levels due to combined wanted-unwanted sounds. Leung et al. compared the three models in their ability for predicting the annoyance level due to the combined water-road traffic sound, suggesting that compared with the energy summation model and the modified energy difference model, the independent effects model displayed relatively the best prediction effect [12]. Wang et.al explored if the dissatisfaction level due to the combined water-secondary radiation sound could be well predicted based on three empirical models (the energy summation model, the independent effects model and the energy difference model). The results showed that the independent effects model obtained the equations with relatively the highest coefficient of determination (R²) values [27]. Generally speaking, the empirical models currently proposed were commonly used to predict the levels of negative reaction caused by combined unwanted sounds. However, the research on models suitable for predicting the reaction levels resulting from the combinations of wanted and unwanted sounds is still in its infancy. Furthermore, given the diverse negative emotions individuals exhibit towards noise in real-world scenarios, previous studies proposed various reaction evaluation indexes, including annoyance, dissatisfaction, depression, discomfort, and other subjective indexes. These indexes are mutually independent and crucial in characterizing the multifaceted negative impacts of noise. Consequently, there is a need for research focusing on these multi-dimensional reaction evaluation indexes. However, the previously proposed combined sound reaction models concentrated on predicting the total annoyance or dissatisfaction. Since annoyance and dissatisfaction are only two types of negative reaction evaluation indexes, it remains to be investigated whether these models can be applied to assess other MNR as well.

Given all these, the question arises whether the MNR due to secondary radiation noise could be moderated by adding different types of water sounds. Wang et al. contended that the subjective loudness, depression, discomfort, and dissatisfaction capture indoor secondary radiation noise reactions better compared to the rumble loudness, low-frequency reaction, annoyance, and non-acceptance. These indexes were defined as critical reactions due to secondary radiation noise [28]. To devise strategies for mitigating these critical negative reactions, this study explored the regulatory effects of incorporating water sounds. Specifically, firstly, this study analyzed the effects of WSNR, reaction type, and the type of added water sound on the MNR due to the combined water-secondary radiation sound. The second objective was to establish a series of optimal models for the different indexes, with the aim of individually predicting the levels of different negative reactions, based on the previously proposed empirical models for combined sound reaction. Finally, according to the optimal models, this study identified the masking mechanisms of different negative reactions. These findings offer a framework for evaluating how different types of water sounds can mitigate the MNR caused by secondary radiation noise.

2 Method

2.1 Preparation of acoustic stimuli

A series of listening tests were conducted to assess the levels of participants’ MNR. In these tests, four types of water sounds – fountain sound, stream sound, water-drop sound, and waterfall sound—were individually incorporated into the secondary radiation noise resulting from indoor vibration. Participants were exposed to a series of combined sound samples before being required to cast their votes for MNR. For the purpose of collecting binaural secondary radiation noise samples, a high-rise office building situated in proximity to Metro Line 4 in Guangzhou, China, was chosen as the collection site. This location is vulnerable to the impact of secondary radiation noise, particularly on the lower floors. Metro Line 4 is a representative metro trunk line in China, operating with a mean speed of approximately 50 km/h and a maximum speed reaching nearly 90 km/h. The building under investigation is situated near a curved track, which comprises a monolithic roadbed, and this track abuts an underground island platform. Besides, the nearest horizontal distance from the measuring point to Metro Line 4 measures approximately 6 m. Meanwhile, the minimum vertical distance between the space occupied by the measuring point and Metro Line 4 stands at approximately 24 m. The secondary radiation noise sample was recorded in a break room located on the second floor, a typical cubic space measuring 4 m in length, 5 m in width, and 4 m in height. The floor was decorated with marbles, the walls with planks and terrazzo, and the ceiling with block materials. In addition, the reverberation time data measured in the break room was listed in Table 1. It can be seen that when frequency was no more than 400 Hz, the reverberation time maintained within 1.3 s; when frequency was higher than 400 Hz, the reverberation time stayed at below 0.9 s.

To minimize the disturbance from other noise sources during data collection, the secondary radiation noise was recorded during the non-opening hours preceding the morning rush hour (7:30 a.m. to 8:00 a.m.). During this time, the occupancy rate of room was relatively low, and there were minimal indoor and outdoor disturbance sounds, ensuring a low background noise level of approximately 40 dBA. This means the collected secondary radiation noise data was mainly caused by metro operation and hardly influenced by other noises. Every three to five minutes, the underground metro train passes through the tunnel near the high-rise office building, causing rumbles within the indoor environment accompanied by the vibration of structures and objects. When these phenomena occur in the indoor environment, which indicates that secondary radiation noise is occurring, people can clearly hear the noise and experience the vibration. To collect the samples of binaural secondary radiation noise, a handheld binaural recorder (SQobold 4-channel data collector) was employed for continuous environmental noise recording, as shown in Figure 1. The recorder continually captured sound data from both the left and right ears as time progressed. Subsequently, these data were exported in the form of wave files for further analysis. Before each measurement, a calibrator was used to calibrate the measurement accuracy of recorder. Firstly, the recorder’s two ears were connected to the calibrator. Once the calibrator was activated, the recorder displayed the SPL at its auditory canal. If the SPL fell within the range of 94.0 ± 0.2 dB, the recorder had good measurement accuracy and could be used for on-site measurement. Otherwise, it needed to be adjusted until the SPL fell within the specified range.

Figure 1 Conducting the collection of secondary radiation noise sample (a) with a handheld binaural recorder (b).

Following the standardized procedures for measuring indoor noises [37–39], the recorder was set at least 1.2 m from the ground, 1.5 m from the nearest reflective surface and 1 m from the operator’s torso. Since secondary radiation noise was clearly audible within the break room, this study recorded the approximate onset time of secondary radiation noise. Additionally, by synchronizing this data with the collected sound waveform files (captured at 44.1 kHz with a depth of 16 bits using the head recorder), the secondary radiation noise signal could be identified. In this study, the duration of secondary radiation noise sample was defined as 10 s for the following reasons. For one thing, one previous study [3] proposed that secondary radiation noise was intermittent, and the duration of most typical secondary radiation noise was 10 s. For another thing, this study collected a series of secondary radiation noise samples emanating from high-rise buildings along the metro lines in Guangzhou. It was discovered that most of these noise samples lasted for 10 s, effectively capturing virtually all relevant information related to the secondary radiation noise generated by metro operation, including train entries, approaches, and departures. This means that a 10-s snippet of secondary radiation noise is sufficient to represent the typical duration of exposure that individuals encounter in their daily lives. Consequently, the duration of binaural secondary radiation noise samples in this study was standardized to 10 s. As for the semantic content of secondary radiation, the collected secondary radiation noise reflected the change of indoor acoustic environment caused by the train’s movement and departure from the building. Generally, as the train approached the building, the level of secondary radiation noise gradually increased, peaking when the distance between the train and the building was at its minimum. Subsequently, as the train moved away, the level of secondary radiation noise gradually decreased. Primarily caused by varying sound reflection patterns on the room walls due to the position of head, there were minor differences between the secondary radiation noise data of left and right ears in the break room.

For the collections of four types of water sounds, the monaural samples of fountain sound, stream sound, water-drop sound and waterfall sound were acquired from a professional audio website [40], where many studies downloaded sound samples to conduct listening experiments [41, 42]. For this study, the keyword “water sound” was entered in the website search bar, and the four types of water sound samples were selected from a large number of sound samples. After downloading, no acoustic processing was performed on the sound samples. Among the four types of water sounds, the water-drop sound refers to the intermittent clicking noise produced when water drops hit a surface, occurring approximately every second. However, other types of water sounds are continuous in nature. For instance, the fountain sound generates a “gurgling” sound, while the stream sound mimics the sound of water flowing at a slower speed, and the waterfall sound is characterized by the sound of water falling at a fast speed. Considering that the duration of secondary radiation noise was 10 s, the masking time of water sounds was also set to 10 s, and each water audio was intercepted as a 10-s sample. The reasons for selecting these four types of water sounds as maskers are as follows. Firstly, they are quite commonplace in daily lives and have been extensively utilized to mask the reactions caused by road traffic noises, exhibiting noteworthy effects [12, 15, 16, 43]. Consequently, they served as viable options for masking the negative reactions due to secondary radiation noise. Secondly, one previous study divided water sounds into three groups, water structures, moving water structures and fountains [44], among which moving water structures and fountains are commonly found in natural environment. Therefore, for the purpose of analyzing the influence of the type of added water sound on the masking effect, this study selected three representative water sounds from moving water structures, namely stream sound, water-drop sound and waterfall sound, and a typical fountain sound from fountains. Another previous study put forward the unique auditory characteristics of different types of water sounds [16]. Among the four, a fountain is water that ejects from the ground, a stream is flowing water with low velocity, a water droplet is a droplet falling from above, and a waterfall is water that falls rapidly. This study selected water sound samples that were consistent with previous research descriptions to conduct the listening experiment.

Due to the minor differences between the secondary radiation noise data of the left and right ears, Figure 2 presents the spectra of monaural sounds, including the fountain, stream, waterdrop, and waterfall, as well as the spectra of binaural secondary radiation noises in the third-octave band, all measured when binaural equivalent A-weighted sound level (L_Aeq) reaches 65 dBA. Following the previous studies [45, 46], binaural L_Aeq is defined as the energetic average of left and right ear values. In Figure 2, the spectra of secondary radiation noise in the left and right ears were quite similar. That is, the binaural A-weighted SPLs increased significantly from 20 Hz, reached their highest levels at 100 Hz, subsequently decreased sharply until 160 Hz, and then decreased slowly towards 8 kHz. As for water sounds, the A-weighted SPL of fountain sound exhibited a certain degree of fluctuation in the low-frequency range, reached its highest value in the middle frequency band and went down obviously from 5 to 8 kHz. Compared with other sounds, the stream sound showed obvious the lowest A-weighted SPLs in the low frequency band and the highest A-weighted SPLs from 5 to 8 kHz. The A-weighted SPL of water-drop sound was obviously higher in the middle frequency band and fluctuated greatly in the middle band in particular. The A-weighted SPL of waterfall sound stayed almost constant from 500 to 4000 Hz before plummeting from 5 to 8 kHz. Figure 3 shows the normalized time domain spectrum of binaural secondary radiation noises and monaural water sounds, it can be seen that the binaural levels of secondary radiation noise (Fig. 3a) gradually increased as time progressed, almost peaking at the midpoint of time domain. Subsequently, as time continued to increase, the noise levels gradually decreased. The levels of fountain sound (Fig. 3b) and stream sound (Fig. 3c) reached intermittent peaks over time. The water-drop sound (Fig. 3d) intermittently emerged. On the other hand, the level of waterfall sound (Fig. 3e) exhibited no significant change over time.

Figure 2 Spectra of binaural secondary radiation noises (a) and four monaural water sounds (b) under binaural LAeq of 65 dBA.

Figure 3 Normalized time domain spectrum of binaural secondary radiation noises (a), monaural fountain sound (b), stream sound (c), water-drop sound (d), and waterfall sound (e).

2.2. Experimental design

In this study, the auditory experiments were conducted using the HD580 model of headphones from the brand Sennheiser, called Sennheiser’s HD580 headphones. This specific model boasts a frequency range of 12 Hz to 38 kHz, along with a nominal impedance of 300 Ω. With the aim of avoiding the influence of headphone frequency response on the listening data to the greatest extent, frequency response calibrations were conducted for the headphones. The time-domain data of binaural sine sweep signals generated in the software Audition and played by the headphones were recorded using an artificial head, a specialized device designed for binaural sound recording that can provide L_Aeq measurements at the ear canals. Following that, by convolving the time-domain data with the inverse filter data of sine sweep signals, the headphone impulse response data were determined. Subsequently, the time-domain data of secondary radiation noises and water sounds would convolve with the inverse filtered data of headphone impulse response. This process allowed us to obtain sound samples that underwent frequency response calibration. Finally, the samples were manipulated only in L_Aeq without spectral adjustment, and the L_Aeq of sound samples played by the headphones was examined by the artificial head.

As for the frequency response curve characteristics of the headphones, the binaural frequency response curves of the headphones tend to be relatively flat when frequency exceeds approximately 60 Hz and remains below approximately 12,000 Hz. However, they exhibit curved shapes when frequency falls below approximately 60 Hz or exceeds approximately 12,000 Hz. This implies that, due to the constraint associated with the frequency response curves of the headphones, sounds within the lower frequency range (roughly below 60 Hz) cannot be faithfully reproduced. Nonetheless, even though indoor vibration-induced secondary radiation noises are typically low-frequency, primarily ranging from 20 to 200 Hz, headphones were still utilized in this study for playback purposes. This decision was made given the challenge associated with accurately reproducing low-frequency content in an experimental setting. For instance, utilizing large-sized speakers to replay low-frequency noise in an auditory test booth could potentially introduce resonance-induced sound coloration issues, ultimately leading to sound signal distortion [47]. Nonetheless, it is worth noting that a limitation of this research was the use of headphones for reproducing the low-frequency noise.

Given that the binaural exposure levels of secondary radiation noise typically ranged from 50 to 65 dBA in most spaces susceptible to such noise in high-rise buildings adjacent to metro lines [28], and drawing on one previous research on road traffic noise masking [12], three higher LAeq levels were selected for the global LAeq of combined sound clips: 55 dBA, 60 dBA, and 65 dBA. The WSNRs of secondary radiation noise and specific water sound were defined to change from −9 to 6 dBA, with an interval of 3 dBA. A positive WSNR indicated that the binaural L_Aeq of specific water sound was higher than that of secondary radiation noise, while a negative value signified the reverse. Finally, 72 combined sound samples, each consisting of 18 (3 × 6) sound clips representing different types of combined secondary radiation-water sound, were formulated for the auditory experiments. Each sample was 10 s long.

2.3 Conduction of auditory experiment

For the auditory experiment, this study chose the auditory test booth located at South China University of Technology as the site. This enclosed cuboid space measures approximately 4 m in length, 8 m in width, and 4 m in height. The background L_Aeq of such a room was relatively low at about 25 dBA. The surroundings and roof of the room were decorated with white latex paint, and the floor of the room was decorated with marble. There was no window inside the room, and the only facilities in the room were a table and a chair. Within the auditory test booth, the magnitudes of air temperature and relative humidity were fixed, at about 20 °C and 40%, respectively. The brightness of the sound playback screen on the computer was also fixed, at around 50%. Each sound source was replayed through manual playback. In order to avoid visual factors affecting the listening results, the participants were required not to see the sound waveforms before listening to sound samples. Only one subject participated when conducting each listening experiment. Before the experiment began, each subject was required to sign an experimental consent form addressing ethical considerations. It was emphasized in the form that the experiment solely involved the investigation of personal reactions, no personal information would be collected, and the research results would be used exclusively for academic purposes.

In order to make each subject understand the experimental questions, the meaning of each question would be explained through oral training, and with the aim of verifying the effectiveness of description, a pre-experiment was organized before each formal experiment. In such a pre-experiment, a combined sound sample was played, and each participant was required to conduct MNR evaluations on the sound sample. Once the participants understood the meaning of each question and provided their judgments, the listening experiment would officially commence. During the experiment, the participants were instructed to sit in front of a desk and imagine themselves studying in their daily lives. Each participant was presented with all 72 combined sound samples in a randomly assigned order, without any weighted design.

To provide valuable insights for mitigating the adverse effect of secondary radiation noise arising from indoor vibrations, this study employed the subjective evaluation indexes used for investigating the reactions due to secondary radiation noise [28]. Specifically, this study explored the evaluation indexes pertaining to low-frequency noise reactions, including rumble loudness, low-frequency reaction, and depression, as well as indexes related to noise reactions including subjective loudness, annoyance, discomfort, non-acceptance, and dissatisfaction. Rumble loudness and low-frequency reaction respectively indicate the perceived intensity of the rumbling and low-pitched sounds produced by metro operation; Depression refers to the degree of emotional dullness; Subjective loudness demonstrates the sound intensity experienced by human ear; Annoyance and discomfort respectively represent the degree of troubled and uncomfortable reactions induced by noise; Non-acceptance and dissatisfaction are psychological constructs related to individual expectations, respectively representing the extent to which individuals do not accept and are unsatisfied with the quality of noise environment. Regarding the definition of the levels of MNR, previous studies proposed two common methods, one is to use an absolute scale, and the other is to use a relative scale. Given the number of listening samples in this study (a total of 72 samples), using relative scales to evaluate the levels of MNR would take a lot of time, which is likely to reduce the quality of listening. Given that previous extensive auditory experiments, which achieved good evaluation results, adopted absolute scales to define reaction levels [12, 36, 48, 49], this study also utilized absolute scales to assess the levels of MNR.

In terms of defining the absolute scale, it is quite common to employ either a five-level scale [50, 51] or an eleven-level scale [52, 53]. This study conducted a pre-experiment to assess the applicability of various scales and discovered that the eleven-level scale was overly detailed for the purpose of this study, potentially leading to confusion among participants. Consequently, a five-level verbal scale was utilized to define the participants’ levels of MNR towards the combined water-secondary radiation sound. For rumble loudness, the five grades were labeled “quite weak”, “weak”, “moderate”, “strong” and “quite strong”; For other perceptual evaluation indexes, the five grades were labeled “not at all”, “slightly”, “moderately”, “very” and “extremely”. Table 2 shows the key questions asked in the questionnaire and the scales used. For each participant, it took approximately three minutes to understand the exact meaning of each question. Each participant had 15 s to record their own levels of MNR for each question (Fig. 4) before moving on to the next sample. In order to minimize the decline of response quality, the experiment contained two breaks of 5–10 min to relieve psychological and physical exhaustion, and each participant was asked to listen to all the combined sound samples and complete the whole experiment in around 50 min.

Figure 4 Conducting questionnaire survey in auditory experiment.

A total of 79 participants were recruited for the auditory experiment, and all the participants declared that they had good hearing abilities. The numbers of male and female participants were similar, at 40 and 39 respectively. The participants aged between 20 and 40 years old, and the proportions of subjects aged 20–24, 25–29, 30–34 and 35–40 were 64.6%, 31.6%, 0.0%, and 3.8%, respectively. The education levels of participants were relatively higher, the numbers of undergraduates, postgraduates and doctoral students being 6, 62 and 11, respectively. Each participant was given a small payment after finishing the whole auditory experiment.

2.4 Combined sound reaction models

Building upon a prior study that focused on road traffic noise masking [12], this study compared the predictive capabilities of three models: the energy summation model, the independent effects model, and the energy difference model, in estimating the levels of MNR resulting from the masking of secondary radiation noise using water sounds. This section provides a concise overview of the three models that have been proposed for assessing the reaction level induced by combined sound. The first is the energy summation model, in which an energy sum of separate sounds is assumed to contribute to total reaction level. The second is the independent effects model, where total reaction level is predicted from separate sounds. The third is the energy difference model, which is derived from the energy summation model and incorporates a correction index that takes into account the difference in L_Aeq between separate sounds.

2.4.1 Energy summation model

This model indicates that total reaction level (P_T) is due to global L_Aeq:

(1)

where P_T is the negative reaction level due to combined sound, and L_T is global L_Aeq predicted as the total energy of separate sounds. This model is based on the theory that the reaction level induced by combined sound can be calculated based on energy sum.

2.4.2 Independent effects model

This model indicates that total reaction level (P_T) is due to separate sounds:

(2)

where P_T is the negative reaction level due to combined sound, while L₁, L₂, …, L_n are the L_Aeq values of separate sounds. This model represents the theory that total reaction level is the result of separate sounds, and the model is regarded as a linear regression model that captures the effects of individual noise levels.

2.4.3 Energy difference model

This model indicates that total reaction level (P_T) is due to global L_Aeq and the difference in L_Aeq between separate sounds:

(3)

The model incorporates the difference in L_Aeq between two separate sounds as a correction factor. This model can only be used in the conditions containing two types of sound sources. The index meanings in the energy summation and the independent effects models apply to the energy difference model as well.

The energy summation model holds that reaction levels are meaningfully determined by the total noise level. However, this phenomenon is not typical in response investigations, as it assumes that the potential to evoke reactions is identical across combined sounds [29]. Therefore, this assumption has been frequently questioned [29, 32]. In contrast, the independent effects model allows for the contribution of the change in one sound exposure level to the total reaction. Numerous studies demonstrated that this model was the most effective in predicting the reaction levels resulting from combined sounds [12, 29]. The energy difference model introduces an absolute L_Aeq difference based on the energy summation model, although some studies did not find support for the applicability of this model [53–56].

2.5 Statistical analysis

As stated in the Introduction, given the diverse negative reactions individuals exhibit to noise, this study chose eight evaluation indexes of negative reaction: rumble loudness, low-frequency reaction, depression, subjective loudness, annoyance, discomfort, non-acceptance, and dissatisfaction. The aim was to investigate the diverse negative emotions towards secondary radiation noise. This section tested the effectiveness of the existing data by analyzing the reliability and validity related to the votes of these eight negative reactions. The results showed that the alpha reliability coefficient was 0.96 and the KMO validity coefficient was 0.92, and the significance coefficient of Bartlett’s test of sphericity was 0.000, which is obviously below 0.05. The above findings demonstrate that the votes of MNR possessed sufficient reliability and validity, rendering them applicable for subsequent analyses.

The votes of MNR were examined if they belonged to normal distributions based on normality tests. The p-values for votes of MNR according to Kolmogorov-Smirnov tests were all below 0.05, indicating that the votes of MNR should be considered non-normal data. Furthermore, given that the votes for MNR exhibited non-normality and that individual listeners’ judgments were dependent, as each evaluated the stimuli based on their own subjective scale, this study employed the Friedman test, which is designed to assess differences across multiple related samples without assuming a normal distribution, to determine whether a specific factor significantly influenced the negative reaction votes. Moreover, following the construction method of three models chosen for this study, multiple linear regression analyses were employed to develop the prediction models for the levels of MNR. The R² values of models were introduced to assess their predictive capabilities.

3 Results

A previous study revealed that, among the eight subjective indexes examined, the subjective loudness, depression, discomfort, and dissatisfaction were more effective in reflecting the impacts of indoor secondary radiation noise than the rumble loudness, low-frequency reaction, annoyance, and non-acceptance. These indexes were mutually independent and were therefore designated as critical reactions to indoor secondary radiation noise [28]. The findings of this study aimed to provide invaluable information for screening optimal water sounds that alleviate these critical reactions, and for understanding how various water sounds mitigate them. Specifically, the results of this study were organized into three parts. The first part (Sects. 3.1–3.3) explored how different factors influenced the MNR in the context of combined secondary radiation-water sound. The second part (Sect. 3.4) established the optimal prediction models for the different indexes related to critical reaction levels, enabling the predictions of critical reaction levels following the addition of water sounds to secondary radiation noise. Finally, the third part (Sect. 3.5) analyzed the masking mechanisms underlying critical reaction levels, utilizing the optimal prediction models for the different indexes. This analysis contributed to the development of targeted strategies aimed at minimizing the critical negative reactions associated with secondary radiation noise.

3.1 WSNR and reaction level

Firstly, to determine whether WSNR would affect the levels of MNR, this section employed the Friedman test (reasons outlined in Sect. 2.5) to investigate whether there was a significant difference in each negative reaction level across varying WSNR conditions. This study utilized the testing module designed for multiple correlated samples within the non-parametric testing framework of the SPSS software to conduct the Friedman test. Specifically, each negative reaction level was categorized into six groups according to WSNR value, which served as the examined variables, while the listener, who used their own scale to evaluate sound samples, functioned as a block variable. Upon scrutinizing the results of the non-parametric tests, the Friedman test yielded an asymptotic significance value below 1E-5 for each negative reaction. This “asymptotic significance” refers to an approximation that is particularly useful for large sample sizes, such as those employed in this study. The asymptotic significance level represents the significance value calculated for detecting difference based on this theory. Since this study aimed to simultaneously test four independent hypotheses on the same dataset, specifically examining whether there was a significant difference in each reaction level under different WSNR, global L_Aeq, reaction type, or the type of added water sound, the Bonferroni correction was applied. This correction is a rigorous technique for defining a significance threshold suitable for scenarios where the number of factors being investigated is fewer than 10. In this study, considering the four independent hypotheses tested on the same dataset, an adjusted significance threshold of 0.0125 (equal to 0.05 divided by 4) was uniformly applied as the significance threshold for all four tests of difference significance conducted in Sections 3.1–3.3. Since this adjusted significance threshold was higher than the observed asymptotic significance value of 1E-5, it could be concluded that the difference in WSNR resulted in a significant difference in each level of negative reaction. Accordingly, the first section intended to explore the impacts of WSNR on the MNR due to the combined water-secondary radiation sound in detail.

To further investigate, this section employed the Friedman tests to examine whether global L_Aeq significantly affected each negative reaction level. Each negative reaction was categorized into three groups based on global L_Aeq level and were included as the examined variables, while the listener was treated as a block variable. The analysis results revealed that, for each negative reaction, the asymptotic significance level derived from the Friedman test was less than 1E-5. This value was substantially lower than the adjusted significance threshold of 0.0125, set after applying the Bonferroni correction. This finding indicated a statistically significant difference in the level of each negative reaction across varying global L_Aeq levels. Consequently, when analyzing the influence mechanisms of WSNR on negative reactions, it is imperative to separately investigate the evaluation results under different global L_Aeq levels. Furthermore, this analytical approach can also be effectively applied to subsequent discussions in Sections 3.2 and 3.3, pertaining to the influences of other factors on the MNR.

By averaging the subjective loudness, depression, discomfort, and dissatisfaction levels under various WSNR conditions, at global L_Aeq levels of 55, 60, and 65 dBA, respectively, the mean MNR levels for these scenarios were presented in Figure 5. It can be seen that the mean levels of MNR remained basically unchanged for global L_Aeq of 55 dBA. Similarly, for global L_Aeq of 60 and 65 dBA, and WSNRs ranging from −9 to −3 dBA, the mean levels remained basically stable. However, the decline in the mean levels was observed when global L_Aeq was 60 or 65 dBA and WSNR exceeded −3 dBA but did not exceed 6 dBA. This suggests that to effectively reduce the levels of MNR at global L_Aeq of 60 and 65 dBA, it is necessary for the difference between the binaural L_Aeq of water sound and that of secondary radiation noise to exceed −3 dBA. Furthermore, the lowest mean levels of MNR were observed when WSNR reached 6 dBA. The above results also suggested that when predicting the mean levels of MNR due to the combined water-secondary radiation sound, the decline at global L_Aeq of 60 and 65 dBA when WSNR was larger than −3 dBA and no greater than 6 dBA ought to be considered.

Figure 5 Mean levels (M) and standard deviations (SD) of specific negative reaction (subjective loudness (a), depression (b), discomfort (c) and dissatisfaction (d)) votes under different WSNRs and global LAeq.

Figure 5 further illustrates the standard deviations of the votes for MNR across various WSNRs and global L_Aeq levels. In this study, the analysis module for mean value in SPSS software was employed to compute the standard deviations of the data. It can be seen that as global L_Aeq increased, the standard deviation generally rose, indicating that the data became more dispersed at higher global L_Aeq levels. Additionally, for each negative reaction where global L_Aeq remained constant, the majority of standard deviations for specific reaction votes showed smaller differences across different WSNRs, suggesting that WSNR had a limited impact on the dispersion of data.

3.2 Reaction type and reaction level

This section aimed to investigate whether the type of reaction would influence the levels of MNR. To achieve this, the Friedman test was firstly utilized to determine whether there was a significant difference among the levels of MNR. In conducting the Friedman test, the listener served as a block variable, and the four different negative reaction levels served as the examined variables. The results of the difference tests revealed that the asymptotic significance value fell below 1E-5, which was significantly lower than the adjusted significance threshold of 0.0125 after applying the Bonferroni correction, indicating the existence of a significant difference among the four negative reaction levels. Consequently, the subsequent portion of this section was dedicated to comparing the disparities observed in the levels of MNR.

With regard to the comparison method, some previous studies proposed analyzing the differences between different reactions by comparing the mean data of reaction levels under the same environmental conditions [57, 58]. Based on this approach, this study analyzed differences in MNR using mean level data within the same global L_Aeq conditions. The steps of data processing are as follows. Initially, each reaction vote was categorized into four groups based on the type of added water sound. Subsequently, within each category, the mean votes for each negative reaction were calculated across different WSNRs corresponding to each global L_Aeq level. This section compared the differences in the mean levels of MNR resulting from the addition of specific water sounds. Given that this section focused solely on analyzing the impact of reaction type as a single factor, the impact of WSNR was not addressed. Since the mean data was collected under identical WSNR environments ranging from −9 to 6 dBA, the analysis results pertaining to this single factor should be considered valid.

Figure 6 shows the mean levels of MNR under each global L_Aeq levels after adding each type of water sound. It can be seen that the mean subjective loudness levels were generally the highest across the increasing global L_Aeq range, regardless of the type of added water sound. This suggests that even when subjects perceived the sound environment to be noisy, their levels of depression, discomfort, and dissatisfaction were relatively lower. Among the four water sound types, the addition of water-drop sound exhibited the smallest disparities between the mean subjective loudness level and the mean levels of other negative reactions. Furthermore, as illustrated in Figures 6a and 6c, the mean levels of depression, discomfort, and dissatisfaction were relatively comparable when the fountain sound or water-drop sound was introduced at global L_Aeq of 55 dBA. However, as global L_Aeq increased to 60 and 65 dBA, the mean depression level slightly became higher than the mean discomfort level and mean dissatisfaction level, while the mean discomfort level remained similar to the mean dissatisfaction level. In addition, as shown in Figures 6b and 6d, when the stream sound was added, the mean depression level slightly exceeded the mean discomfort level and mean dissatisfaction level at global L_Aeq of 60 dBA. In other cases, with the addition of either stream or waterfall sound, the mean levels of depression, discomfort, and dissatisfaction remained basically similar as global L_Aeq rose from 55 to 65 dBA.

Figure 6 Mean levels (M) and standard deviations (SD) of MNR votes under different global LAeq after adding each type of water sound (fountain sound (a), stream sound (b), water-drop sound (c) and waterfall sound (d)).

Figure 6 further illustrates the standard deviations associated with the levels of MNR after incorporating specific types of water sound across various global L_Aeq levels. As global L_Aeq increased, the standard deviation generally rose, also indicating that the higher the global L_Aeq, the more dispersed the data became. Regardless of the type of added water sound, the standard deviations for most MNR levels exhibited relatively small differences when global L_Aeq remained constant. This suggests that the type of negative reaction had minimal impact on the dispersion of data.

3.3 Type of added water sound and reaction level

Firstly, to assess whether the type of added water sound affected the levels of MNR, this section also selected the Friedman test to examine whether there was a significant difference in each negative reaction level when different types of water sounds were added. Specifically, each negative reaction level was divided into four groups based on the type of added water sound, and these were designated as the examined variables. Additionally, the listener was designated as a block variable. The test results indicate that the asymptotic significance value for each negative reaction was below 1E-5, which was lower than the Bonferroni-adjusted significance threshold of 0.0125. Therefore, a significant difference was found in the level of each negative reaction when the type of added water sound was different. Therefore, the third section aimed to compare the levels of specific negative reactions after incorporating various types of water sounds.

Concerning the comparison approach, the data processing method employed in this section aligned with that used in Section 3.2. It is important to note that, although the figures presented in Sections 3.2 and 3.3 were based on the same mean data, the focus of these two sections differed. Specifically, this section aimed to explore the influence of the type of added water sound on the reaction due to combined sound, while the aim of Section 3.2 was to examine the influence of reaction type. Given that this section primarily analyzed the impact of the single factor, namely the type of added water sound, the influence of WSNR was also not included in the discussion. Even without considering the impact of WSNR, the mean data was calculated within the same WSNR environments, ranging from −9 to 6 dBA. This ensured that the analysis results pertaining to this single factor remained valid.

Figure 7 illustrates the mean levels of specific negative reactions under each global L_Aeq level when various water sounds were added. It can be seen that as global L_Aeq increased from 55 to 65 dBA, the mean levels of MNR remained the highest when the waterfall sound was added. This indicates that the waterfall sound was the least effective in regulating the MNR caused by secondary radiation noise. Additionally, at global L_Aeq level of 55 dBA, the mean levels of MNR were relatively similar across the fountain, stream, and water-drop sounds. However, as global L_Aeq rose to 65 dBA, the lowest mean levels of MNR were observed when the water-drop sound was added. This suggests that the water-drop sound was the most effective in regulating the MNR under higher combined sound L_Aeq. At global L_Aeq of 65 dBA, the mean levels of MNR were higher with the addition of stream sound compared to the fountain sound, focusing on subjective loudness, discomfort, and dissatisfaction. This suggests that, in the context of higher global L_Aeq of combined sound, the fountain sound was more effective in managing the MNR than the stream sound, focusing on subjective loudness, discomfort, and dissatisfaction.

Figure 7 Mean levels (M) and standard deviations (SD) of specific negative reaction (subjective loudness (a), depression (b), discomfort (c) and dissatisfaction (d)) votes under different global LAeq after adding four types of water sounds.

Figure 7 also demonstrates the standard deviations of each negative reaction after the addition of four different water sounds across varying global L_Aeq levels. As global L_Aeq increased, the data exhibited greater dispersion, which was evident in a general upward trend in the standard deviation. Furthermore, when global L_Aeq remained constant and different types of water sounds were introduced, the differences in the majority of standard deviations for specific negative reaction votes were relatively smaller. This observation suggests that the type of added water sound had a minimal impact on the dispersion of the data.

3.4 Optimal prediction model for reaction level

The fourth section was devoted to the development of optimal prediction models for the different indexes pertaining to the levels of MNR caused by the combination of water and secondary radiation sounds. To establish the prediction models, this study employed the linear regression module in SPSS software. Due to the significant difference observed in the levels of MNR (with significance value below 0.0125) and the significant influence of the type of added water sound on each reaction level (with significance values below 0.0125), prediction models were developed for each reaction level following the introduction of each water sound type. Furthermore, according to prior studies [12, 27], three different physical model forms were chosen for evaluation: the energy summation model, the independent effects model, and the energy difference model. These models were assessed based on their ability to predict the levels of MNR. Among them, the energy difference model was modified by eliminating the absolute sign for the “Difference in L_Aeq between two sources”. This modification was because that unlike previous studies, this research focused on a wanted sound source (water sound) and an unwanted sound source (secondary radiation noise) rather than two unwanted sound sources. In addition, a prior study [12] suggested that incorporating additional significant influencing factors into the three different physical model forms could enhance the accuracy of prediction models for the different indexes. Given that WSNR Threshold had a significant impact on the levels of MNR (with significance values below 0.0125), the relevant acoustic factor Threshold as an explanatory variable was introduced in the model forms. To mitigate the issue of multicollinearity, the variable Threshold was excluded from the modified energy difference model.

There are two approaches to establish the prediction model for reaction level: predicting individual reaction level and predicting mean reaction level [3]. In this study, the R² values associated with the prediction models for individual MNR levels were relatively low (ranging from approximately 0.2–0.4). However, the prediction models for mean negative reaction levels achieved significantly higher R² values, exceeding 0.8. Thus, in order to more effectively evaluate the reaction levels based on models with superior fitting capabilities, the prediction equations for the mean levels of MNR were developed. The method for developing the prediction equations involved utilizing the acoustic parameters of each combined sound sample, with the aim of predicting the mean negative reaction level of 79 participants corresponding to each combined sound sample. The detailed method was as follows. This study encompassed a total of 72 combined sound samples, including 18 samples per type of combined water-secondary radiation sound. To develop the prediction model for each reaction level triggered by each type of combined sound, the mean negative reaction level was calculated for each sample across all 79 participants. Subsequently, linear regression equations were formulated by linking the mean reaction level to the acoustic parameters of each combined sound sample.

When Threshold was introduced as a variable in the independent effects model, the R² value increments were relatively minor, with growth amplitudes below 0.03. However, when Threshold was added to the energy summation model, the increases in R² values were more significant. Specifically, upon incorporating the fountain sound or water-drop sound, the increase in R² values after adding Threshold ranged from approximately 0.1–0.2. For the stream sound or waterfall sound, the increase was mostly within the range of 0.04–0.1. Furthermore, there were only minor differences observed among the R² values of the refined energy summation models, the refined independent effects models, and the modified energy difference models. Among the three types of models, the refined independent effects models consistently yielded the highest R² values, except in one instance where the refined energy summation model slightly outperformed it in predicting subjective loudness when the fountain sound was added. Consequently, the refined independent effects models were deemed as the optimal prediction models for the different indexes (with a relevant acoustic factor Threshold). Table 3 presents the optimal prediction models for the different indexes. For the prediction models derived from the other two models (the refined energy summation model and the modified energy difference model), please refer to Table A1 in Appendix A.

3.5 Masking mechanism evaluation

After comparing various models, the refined independent effects models were identified as the optimal prediction models for estimating the mean levels of MNR (owing to their nearly highest R² value). Therefore, the subsequent analysis was based on these optimal prediction models, which incorporated the relevant acoustic factor of Threshold. The coefficient values from the optimal prediction models for the different indexes could be used to assess the impacts of individual factors on the mean levels of MNR. A positive coefficient indicated that an increase in the studied factor would lead to a corresponding rise in the mean level of MNR, and vice versa. It can be seen that both increases in the L_Aeq of water sound and secondary radiation noise contributed to rises in the mean levels of MNR. However, the mean levels of MNR were more influenced by the L_Aeq of secondary radiation noise than by the L_Aeq of water sound, as evidenced by the higher coefficient values for the L_Aeq of secondary radiation noise.

Among the various water sounds, a 1 dBA increase in the L_Aeq of waterfall sound had the most significant impact on elevating the mean levels of MNR, with the highest coefficient values associated with the L_Aeq of water sound. Conversely, the water-drop sound exhibited the least significant impact, with the lowest coefficient values associated with the L_Aeq of water sound. Furthermore, a 1 dBA increase in the L_Aeq of secondary radiation noise had the most pronounced effect on increasing the mean levels of MNR associated with the combined stream-secondary radiation sound, marked by the highest coefficient values for the L_Aeq of secondary radiation noise. When each type of water sound was introduced, a 1 dBA increase in the L_Aeq of secondary radiation noise resulted in the most prominent increases in the depression level, with the highest coefficient values for its L_Aeq. Meanwhile, a 1 dBA increase in the L_Aeq of water sound had the most significant effects on enhancing the subjective loudness level, characterized by the highest coefficient values for the L_Aeq of water sound, while having the least significant effects on enhancing the depression level, indicated by the lowest coefficient values for the L_Aeq of water sound. Additionally, under the conditions where global L_Aeq was 60 or 65 dBA and WSNRs ranged from −3 to 6 dBA, the addition of any of the four types of water sounds led to decreases in the mean levels of MNR, reflected by negative coefficient values for Threshold. Among these, the decreases in the mean levels of MNR caused by the combined stream-secondary radiation sound were the least evident, marked by the lowest Threshold coefficient values, while those caused by the combined fountain-secondary radiation sound were the most significant, characterized by the highest Threshold coefficient values.

Apart from proposing mechanisms by which individual factors influence the mean levels of MNR, the established models can provide valuable information for determining the trade-off ratios rated by participants given the same mean levels of MNR. These trade-off ratios, reflecting the relative preferences of individuals, are determined by the ratio of coefficients, signifying the rate at which one unit of a factor is sacrificed for a unit increase in another factor. For example, the introduction of fountain sound was associated with a trade-off where a 1 dBA reduction in the L_Aeq of secondary radiation noise was deemed equivalent to a 2.4 dBA increase in the L_Aeq of water sound for subjective loudness, 3.8 dBA for depression, 3.1 dBA for discomfort, and 2.9 dBA for dissatisfaction. Table 4 presents a comprehensive overview of such trade-off ratios for each MNR when the four types of water sounds were added.

As shown in Table 4, the addition of water sounds, specifically the fountain, stream, water-drop, and waterfall, optimized the MNR with respect to secondary radiation noise, as evidenced by higher coefficient values for the L_Aeq of secondary radiation noise than those of water sounds. Among the four types of water sound, a 1 dBA reduction in the L_Aeq of secondary radiation noise was deemed equivalent to the maximum increase in the L_Aeq of water-drop sound associated with each negative reaction level, yielding the highest trade-off ratios. Conversely, the same reduction in secondary radiation noise L_Aeq was deemed equivalent to the minimum increase in the L_Aeq of waterfall sound with each negative reaction level, resulting in the lowest trade-off ratios. Additionally, a 1 dBA reduction in the L_Aeq of secondary radiation noise correlated with the maximum increase in the L_Aeq of water sound linked to depression, reflecting in the highest trade-off ratios. However, the same reduction was deemed nearly equivalent to the minimum increase in the L_Aeq of water sound pertaining to subjective loudness, yielding almost the lowest trade-off ratios.

Utilizing the optimal prediction models tailored for the different indexes (Table 2), it was possible to compute the predicted mean levels of MNR resulting from the combined effect of water sound and secondary radiation noise. Figure 8 illustrates the predicted mean levels of MNR caused by combined water-secondary radiation sound. These predicted mean levels were derived by maintaining the binaural L_Aeq of secondary radiation noise at 60 dBA and varying the binaural L_Aeq of water sounds within the range of 53–63 dBA. When incorporating the influence of WSNR into the prediction models, a simplification was made to the underlying mechanism. Specifically, the continuous decrease in negative reaction level was regarded as a single decrement value, forming a correction factor known as Threshold. Nonetheless, despite this simplification, the prediction models achieved satisfactory results. It is noteworthy that the discussion on the variation patterns of predicted reaction levels, influenced by Threshold, remained descriptive. When the WSNR surpassed −3 dBA, the abrupt decline in the mean levels of MNR observed as the L_Aeq of water sounds exceeded 57 dBA indicated that the growth trends of MNR levels tended to decrease. The magnitude of this decrease was linked to the type of added water sound. For instance, compared to other types of water sounds, the growth trends of mean levels of MNR decreased the least when the stream sound was added. On the other hand, when disregarding the effect of Threshold, the MNR levels tended to increase as the L_Aeq of water sounds rose. Furthermore, when the waterfall sound was added, the predicted mean levels of MNR were the highest. In contrast, the water-drop sound led to relatively the lowest predicted mean levels of MNR. Moreover, the predicted mean levels of MNR due to the combined fountain-secondary radiation sound were generally lower than those due to the combined stream-secondary radiation sound.

Figure 8 Predicted mean levels of MNR (subjective loudness (a), depression (b), discomfort (c) and dissatisfaction (d)) after adding different LAeq of water sounds to 60 dBA of secondary radiation noise.

4 Discussion

4.1 Influencing factors of MNR

The mean levels of MNR due to the combined water-secondary radiation sound were found to be influenced by WSNR Threshold. Specifically, at global L_Aeq of 55 dBA, as well as for global L_Aeq of 60 and 65 dBA with WSNRs varying from −9 to −3 dBA, the mean levels of MNR remained basically unchanged. However, when WSNR exceeded −3 dBA but was no greater than 6 dBA, at global L_Aeq of 60 and 65 dBA, decline in the mean levels of MNR was observed, and the mean levels of MNR were found to be the lowest when WSNR increased to 6 dBA. This finding deviates from the theory, which suggested that considerable differences in reactions to combined sounds occurred when the sound levels of both sources were similar [12, 29, 59]. Such differences can be attributed to the different acoustic properties of secondary radiation noise and the disparity in the examined global L_Aeq of combined sound. Besides, these phenomena were only observed when global L_Aeq levels were 60 dBA and 65 dBA, but not at 55 dBA. The primary reason for this lies in the fact that, at global L_Aeq of 55 dBA, the mean levels of MNR were relatively lower. Consequently, the increase of water sound L_Aeq did not contribute to obvious reduction in the mean levels of MNR.

This study also proposed that the introduction of four different types of water sounds – fountain, stream, water-drop, and waterfall – all contributed to mitigating the subjective loudness, depression, discomfort, and dissatisfaction associated with secondary radiation noise. The findings echoed previous conclusions that water sounds can improve the emotions triggered by combined sounds [8–16]. Moreover, the type of added water sound was found to affect the optimization effect, with the water-drop sound emerging as the most effective in masking the MNR caused by secondary radiation noise, while the waterfall sound was the least effective. These findings were in line with previous studies aimed at masking road traffic noise, where the water-drop sound was found to be the most effective in enhancing subjective tranquility assessments [60], and the waterfall sound was the least useful in optimizing subjective assessments of peacefulness and relaxation [43]. The observation that water-drop sound was the most effective masking sound might suggest that sounds with significant changes in spectral curve contribute to better masking effects. As for the optimization mechanisms of water-drop sound as the most effective masking sound, at global L_Aeq from 55 to 65 dBA, the mean subjective loudness votes generally remained at the highest levels. Besides this, when global L_Aeq increased to 65 dBA, the mean depression level was slightly higher than the mean discomfort and dissatisfaction levels, with the latter two being comparable. It is worth noting that this study focused on analyzing the mechanisms of individual influencing factors (WSNR, reaction type, and the type of added water sound). Future research should explore the interaction mechanisms between multiple influencing factors for a more comprehensive understanding.

Besides WSNR, reaction type and the type of added water sound introduced, visual factor was believed to potentially influence subjective reactions [61, 62]. This study overlooked the impact of visual factor, and the only scenario provided to the participants consisted of a desk and a chair, excluding any outdoor elements or sound waveform visuals. Therefore, there is a need for numerous further studies to explore the roles of visual factor. For example, it remains to be investigated whether there would be any difference in the levels of MNR if the participants could see the fluctuation images of sound samples or outdoor views, or if the interior decoration is more diverse.

4.2 Prediction models of MNR

This study successfully established a series of optimal models for the different indexes, enabling individual prediction of mean levels of different negative reactions resulting from the introduction of diverse water sounds into the secondary radiation noise caused by indoor vibration. The developed models for the different indexes provided trade-off ratios among individual influencing factors. For instance, when considering the mean subjective loudness level, a 1 dBA reduction in the L_Aeq of secondary radiation noise was deemed equivalent to a 2.4 dBA, 2.9 dBA, 3.9 dBA, and 1.6 dBA increase in the L_Aeq of fountain sound, stream sound, water-drop sound, and waterfall sound, respectively. These conversion metrics facilitate the interpretation of negative reaction effects arising from the combination of water and secondary radiation sounds at objectively measured dBA levels, thereby assisting individuals in making multi-criteria decisions in their daily lives.

This study established a series of models that could individually predict the mean levels of different negative reactions based on three previously proposed physical models: the energy summation model, the independent effects model, and the energy difference model. These models have been widely used to predict the annoyance levels resulting from the combinations of unwanted sounds. The present study evaluated the appropriateness of these three models in individually assessing the mean levels of different negative reactions arising from the combination of a wanted sound (water sound) and an unwanted sound (secondary radiation noise). The analysis results revealed that the refined independent effects models were basically the most effective in predicting the mean levels of MNR when a relevant acoustic variable (Threshold) was introduced. This model was also found to identify as optimal for predicting the annoyance levels triggered by the combined road traffic-water sound [12] and the combined aircraft-road traffic noise [29]. However, it’s worth noting that, in addition to the three combined sound reaction models selected for this study, there exist various other models, such as the response-summation model, summation and inhibition model, and dominant source model. These models were also developed to predict the negative reactions resulting from combined sounds. Consequently, it’s imperative to assess whether these alternative models can better predict the mean levels of MNR.

The three physical model forms examined in this study relied solely on objective acoustic parameters, such as L_Aeq and WSNR, to assess the MNR levels. Previous studies showed that certain psychoacoustic parameters, including loudness and roughness, also played significant roles in influencing the reactions to combined sounds. For instance, Jeon et al. emphasized the importance of sharpness in determining the reactions to the combined road traffic – water sound in urban soundscapes [18]. Lee et al. discovered that the annoyance caused by the combined construction noise was significantly influenced by loudness and roughness [49]. Therefore, it is uncertain whether some specific psychoacoustic parameters have significant impacts on the levels of MNR caused by the combined water-secondary radiation sound. If these factors are proven to be crucial, their integration into prediction models would be necessary to enhance their accuracy.

The study proposed that the MNR caused by secondary radiation noise could be optimized by adding water sounds, referencing prediction models. However, the extent of this optimization remains a separate area of investigation. Due to the avoidance of excessive length in the research content, a thorough analysis of the optimization amplitude was not conducted. Nevertheless, for future exploration, it is imperative to investigate the degree of MNR optimization achieved through the addition of water sounds, by combining the subjective listening results of pure secondary radiation noise. This would serve as a more comprehensive reference for improving the MNR caused by secondary radiation noise. It is worth noting that the optimization effect of specific types of water sounds is linked to their acoustic characteristics, such as spectrum shape. Therefore, future research should delve deeper into how the acoustic characteristics of specific types of water sounds influence the optimization amplitude.

4.3 Limitations

For the auditory experiments, a single sample of secondary radiation noise caused by indoor vibration was selected, along with a single sample for each type of water sound. These combinations were then used to create the combined sound samples. The decision to use single sound samples was based on several considerations. Firstly, regarding secondary radiation noise, this study aimed to collect a typical set of binaural secondary radiation noise samples. The selection criteria are as follows. Given the similarity in train type and operating speed on metro trunk lines, which leads to comparable vibration sources, and the increasing number of high-rise office buildings with frame structures constructed near metro trunk lines, a high-rise office building with a frame structure, adjacent to a metro trunk line (Metro Line 4) in Guangzhou, China, was chosen as the collection site. Furthermore, a relatively enclosed cubic space measuring 4 × 5 × 4 m was selected. This space is a common type found in most office buildings and widely distributed across different floors. The combination of a typical metro vibration source and a typical sound collection space is likely to ensure the representativeness of the secondary radiation noise samples.

Secondly, regarding water sounds, this study also aimed to collect typical water sound samples. Based on some previous studies that identified the types of water sounds [44] and their typical characteristics [16], four common water sounds in the natural environment were selected: fountain, stream, water-drop, and waterfall sounds. These sounds align with the descriptions of typical characteristics provided in previous studies. The decision to use single samples was also influenced by previous auditory masking studies [11, 12], which analyzed reactions after adding a single sample of each type of wanted sound to a single unwanted sound. This approach was adopted to maintain the quality of responses and avoid degradation resulting from a large number of listening samples. Moreover, the evaluation results based on single samples could provide foundations for more in-depth studies in the future.

It is noteworthy that spectral features can influence noise reactions [17, 19, 63]. Consequently, the evaluation results of this study are specific to the secondary radiation noise, fountain sound, stream sound, water-drop sound, and waterfall sound, each characterized by their unique spectral properties. Specifically, the A-weighted SPLs of binaural secondary radiation noises increased from 20 Hz, peaking at 100 Hz, then significantly declined until 160 Hz, and subsequently declined gradually towards 8 kHz. As for the water sounds, the fountain sound exhibited fluctuations in its A-weighted SPL energies in the low-frequency range, emitted the most A-weighted SPL energies in the middle frequency band before a significant drop from 5 to 8 kHz. In contrast, the stream sound exhibited higher A-weighted SPLs from 5 to 8 kHz compared to other samples. The water-drop sound displayed notable fluctuations in its A-weighted SPL, particularly in the mid-frequency band. The A-weighted SPL of the waterfall sound remained relatively stable from 500 to 4000 Hz, but dropped precipitously between 5 and 8 kHz. If the spectral attributes of the secondary radiation noises and water sounds under investigation differ significantly from those observed in this study, the evaluation results may lack sufficient accuracy. Therefore, for future studies, it is crucial to explore a wider range of secondary radiation noises and water sounds with different spectral profiles. This would enable the incorporation of spectral feature as a corrective factor, ultimately leading to more universally applicable outcomes.

Prior to the auditory experiment, a series of samples of secondary radiation noise were collected in high-rise office buildings located along metro trunk lines, which are particularly prone to such noise. The findings revealed that, in most cases, the exposure levels of secondary radiation noise ranged between 50 and 65 dBA [28]. Based on one previous study [12], three relatively higher secondary radiation noise L_Aeq levels (55, 60, and 65 dBA) were selected as global L_Aeq to establish models. This implies that the evaluation results are applicable to global L_Aeq levels falling within the range of 55–65 dBA. However, there are certain scenarios where water sounds are combined with secondary radiation noise, both at lower L_Aeq levels, such as on higher floors, and at higher L_Aeq levels, such as areas close to metro lines. Therefore, it remains crucial to investigate the masking effects of secondary radiation noise at global L_Aeq levels both below 55 dBA and above 65 dBA.

Because it is not easy to setup an experiment accurately reproducing low frequency content, even though the headphones may not effectively reproduce noises within certain low-frequency band due to their non-linear frequency response curves, this study nonetheless employed the headphones to reproduce binaural secondary radiation noise samples, which are typically low-frequency noises. Given the limitations of using the headphones in accurately reproducing low-frequency noise, there is a need to explore more effective sound playback modes that can faithfully reproduce sounds within low frequency range, thereby more accurately reflecting the acoustic environment under on-site condition. This could potentially lead to more accurate evaluation results and improved prediction models.

It is noteworthy that no post-hoc testing, such as pairwise comparison, was conducted following the Friedman difference tests. Consequently, while the significance analysis results from the Friedman difference tests suggested the presence of significant differences in the level of negative reaction across various factors (WSNR, global L_Aeq, reaction type, and the type of added water sound), the specific factor responsible for these differences was not identified. As a result, the detailed interpretation of Figures 5–7 based on the Friedman difference tests, in some sense, remains descriptive only.

This study evaluated the influence mechanisms of combined sound reaction using averaged data (mean or median). The analysis encompassed the results from the Friedman difference test, examining the impacts of various factors including WSNR, reaction type, and the type of added water sound, as well as the construction of prediction models. It is crucial to emphasize that the analysis results presented in this study, based on averaged data, constitute interim findings. The evaluation outcomes, incorporating the influence mechanisms of individual factors, hold significant potential for further exploration. For instance, the application of a linear mixed-effects model is crucial to determine whether significant differences exist among multiple sets of data when considering individual ratings.

5 Conclusions

Based on the auditory experiments conducted in the laboratory condition, this study analyzed the regulatory effects of adding four types of water sounds (fountain, stream, water-drop, and waterfall) on the MNR, including subjective loudness, depression, discomfort, and dissatisfaction, due to secondary radiation noise caused by indoor vibration. The experiment was conducted under three global L_Aeq levels (55, 60, and 65 dBA) and with WSNRs ranging from −9 to 6 dBA. The key findings are presented below.

1. This study developed prediction equations for the mean levels of MNR resulting from the combined water-secondary radiation sound, relying on three combined sound reaction models: the energy summation model, the independent effects model, and the energy difference model. Given that the WSNR exerted a significant influence on the MNR levels, and that these levels declined at global L_Aeq levels of 60 and 65 dBA when WSNR exceeded the range of −3 dBA to 6 dBA, an additional pertinent acoustic factor, WSNR Threshold, was incorporated into the prediction models. Upon including this Threshold in the independent effects model, there were marginal increases in the R² values of the prediction models (with growth amplitudes below 0.03). However, when Threshold was incorporated into the energy summation model, the R² values increaed more significantly (with growth amplitudes below 0.2). With the addition of Threshold, the refined independent effects models nearly attained the highest R² values among the three models, making them the optimal models for predicting the MNR. According to the optimal models, the reduction in the mean levels of MNR due to the WSNR Threshold was most significant for the combined fountain-secondary radiation sound and least significant for the combined stream-secondary radiation sound.

2. The introduction of water sounds was proven to moderate the MNR caused by secondary radiation noise. Among the four tested water sounds, the water-drop sound exhibited the greatest potential for improving the MNR due to high level of combined sound. In contrast, the waterfall sound was the least effective in regulating the MNR as global L_Aeq increased from 55 to 65 dBA. When compared to the stream sound, the fountain sound displayed relatively greater capacities in regulating the MNR, focusing on subjective loudness, discomfort, and dissatisfaction levels caused by high level of combined sound. This indicates that the water-drop sound was the most effective in mitigating the MNR, followed by the fountain sound and the stream sound. The waterfall sound showed the least significant optimization effects. Furthermore, among the four types of water sounds, a 1 dBA reduction in secondary radiation noise was equivalent to the maximum increase in the water-drop sound L_Aeq associated with each negative reaction level, as well as the minimum increase in the waterfall sound L_Aeq. Compared to the fountain sound, a 1 dBA reduction in secondary radiation noise was equivalent to a larger increase in the stream sound L_Aeq pertaining to the depression.

3. As global L_Aeq increased from 55 to 65 dBA, among the four reactions, the mean subjective loudness levels generally remained at the highest. Beyond the subjective loudness, when global L_Aeq stayed at 55 dBA, the mean depression level, discomfort level, and dissatisfaction level were comparable. However, as global L_Aeq increased to 65 dBA, the mean depression level surpassed the mean discomfort level and mean dissatisfaction level when the fountain sound or water-drop sound was added, conversely, the three mean levels remained approximately equal when the stream sound or waterfall sound was added. Furthermore, compared to other negative reactions, a 1 dBA reduction in secondary radiation noise was equivalent to the maximum increase in the L_Aeq of the four water sounds associated with the depression, as well as almost the minimum increase in the L_Aeq of the four water sounds related to the subjective loudness.

Acknowledgments

This work was supported by the School of Architecture of South China University of Technology, which permitted the team to conduct this research. The authors would also like to thank all the participants in the laboratory study.

Appendix A

Funding

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

Conflicts of interest

The authors declare no conflict of interest.

Data Availability Statement

Data are available on request from the authors.

References

All Tables

All Figures

	Figure 1 Conducting the collection of secondary radiation noise sample (a) with a handheld binaural recorder (b).
In the text

	Figure 2 Spectra of binaural secondary radiation noises (a) and four monaural water sounds (b) under binaural LAeq of 65 dBA.
In the text

	Figure 3 Normalized time domain spectrum of binaural secondary radiation noises (a), monaural fountain sound (b), stream sound (c), water-drop sound (d), and waterfall sound (e).
In the text

	Figure 4 Conducting questionnaire survey in auditory experiment.
In the text

	Figure 5 Mean levels (M) and standard deviations (SD) of specific negative reaction (subjective loudness (a), depression (b), discomfort (c) and dissatisfaction (d)) votes under different WSNRs and global LAeq.
In the text

	Figure 6 Mean levels (M) and standard deviations (SD) of MNR votes under different global LAeq after adding each type of water sound (fountain sound (a), stream sound (b), water-drop sound (c) and waterfall sound (d)).
In the text

	Figure 7 Mean levels (M) and standard deviations (SD) of specific negative reaction (subjective loudness (a), depression (b), discomfort (c) and dissatisfaction (d)) votes under different global LAeq after adding four types of water sounds.
In the text

	Figure 8 Predicted mean levels of MNR (subjective loudness (a), depression (b), discomfort (c) and dissatisfaction (d)) after adding different LAeq of water sounds to 60 dBA of secondary radiation noise.
In the text