Characterizing Uncertainty of Violin Mobility Measurements

Knowledge of measurement uncertainty is ontological to any experiment that tests a causal relationship among two or more variables. We have developed a method for quantifying the expected range of deviation among repeated measurements of the impulse response of violins. We measure input mobility by tapping the bridge of a violin with a small modal impact hammer and recording the velocity response of the top plate near the foot of the bridge using a laser Doppler vibrometer; the acoustic response is measured in an anechoic chamber with a similar procedure. Both quantities are functions of frequency, derived from digital Fourier transforms of sampled time-varying signals. The variance of the response at each frequency is calculated for N measurement trials, each of which consists of the average of multiple taps. These are averaged over specific frequency ranges corresponding to vibrational modes of interest and scaled to the largest value within the range. We investigate how the number of taps included in the average for each trial affects the size of the uncertainty values. We also compare the response of individual measurements to the average, with fuzzy plots used to display the deviation. Changes in response due to string tension creep are compared to the base deviation measurements to observe the effect of string tension on the mobility of the violin. The procedure for finding the uncertainty of violin mobility measurements will be used in future research to better determine the effects of playing the violin over time, a process known to violin players as "playing in" the instrument.