*Structural acoustics of good and bad violins*JASA 2008

One of the results or claims there are that better instruments have a lower critical frequency. The critical frequency is the frequency where the bending waves in the wood and the speed of sound in air is the same. The radiation is then peaking in its efficiency. We see this quite clearly in sound reduction measurements and impact noise measurements in the architectural acoustics where the sound reduction curve has a dip and the impact noise curve has a peak in the frequency response. But the effect is not so easy to spot in spectra from violins.

Anyway, I have copied Bissingers data from his figure where he compare the subjective rating and the measured critical frequency (his definition of the critical frequency is a bit different from the classic way, he uses the point for where the regression fitted radiation efficiency fitted line crosses the 0dB line (or 1 in linear scale. The classic critical frequency will lie higher than that by some 1kHz or so)

I enclose the figure with my copied data above. As you see he has grouped the scores into three classes, and he use the average radiation efficiency lines for the bad versus the good and excellent to reach the conclucion that the better violins tend to have lower critical frequencies.

I have tested the data including all of the points for critical frequency against the subjective scores and tested if there is a significant correlation there, and thus: if the slope between subjective rating and critical frequency is significantly different from zero. It turns out it isn't. There is a slope for the regression line, but the slope is not statistically significant.

The correlation coefficient is -0.47, but the p-value is 0,2. If the p-value had been below some 0.05 there would have been a signal there.

A lower critical frequency would idicate a thicker top plate, stiffer wood, or both.