Table 4.
Experimental and numerical results for low-order modes. Mean values and standard deviations are reported for F 1 ≡ A 0, F 2 ≡ T 1, and higher soundboard modes F 3–F 5, along with damping ratios and total mass of the guitars. Numerical standard deviations are taken from stochastic computations in [33] (input-uncertainty ensemble). The required minimum number of pairs is given by Lehr’s rule for a two-sample t-test at α = 0.05 (approx. power 0.8).
| Observables | Scalloped brace (S) | Regular brace (R) | Pairs needed |
|---|---|---|---|
| F 1 (A 0) [Hz] | 102.2 ± (2.7) | 109.8 ± (2.4) | n ≥ 2 |
| Exp. F 2 (T 1) [Hz] | 187 ± (4) | 216.5 ± (5.1) | n ≥ 1 |
| Num. F 2 (T 1) [Hz] | 184 ± (4) | 204 ± (5.1) | n ≥ 3 |
| Exp. F 3 [Hz] | 358 ± (14) | 396 ± (21) | n ≥ 4 |
| Num. F 3 [Hz] | 386 ± (19) | 429 ± (21.5) | n ≥ 3 |
| Exp. F 4 (Dipole) [Hz] | 376.1 ± (16) | 430 ± (15.3) | n ≥ 2 |
| Num. F 4 (Dipole) [Hz] | 406 ± (16) | 440 ± (15.3) | n ≥ 4 |
| Exp. F 5 [Hz] | 549.9 ± (33) | 595.5 ± (28.7) | n ≥ 8 |
| Num. F 5 [Hz] | 548 ± (33.2) | 598 ± (28.7) | n ≥ 6 |
| ζ 1 (%) | 1.7 ± (0.1) | 1.6 ± (0.1) | n ≥ 16 |
| ζ 2 (T1) (%) | 2.4 ± (0.4) | 2.3 ± (0.5) | n ≥ 324 |
| ζ 3 (%) | 1.0 ± (0.2) | 0.9 ± (0.1) | n ≥ 36 |
| ζ 4 (%) | 1.1 ± (0.1) | 1.9 ± (0.7) | n ≥ 4 |
| ζ 5 (%) | 1.1 ± (0.1) | 1.0 ± (0.1) | n ≥ 16 |
| Mass [g] | 1929.2 ± 93 | 1903 ± 105.5 | n ≥ 178 |
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