Favorite problems on acoustic transducers and linear systems theory

• Published in: The Journal of the Acoustical Society of America Vol. 152; no. 4; p. A167
• Main Author: Wilson, Preston S.
• Format: Journal Article
• Language: English
• Published: 01.10.2022
• ISSN: 0001-4966; 1520-8524
• DOI: 10.1121/10.0015905

Practitioners of acoustics sometimes forget how lucky we are that the vast majority of acoustic phenomena and devices we encounter in daily life are linear and solutions using linear systems theory work very well for predicting behavior and designing devices. Typical examples are microphones, loudspeakers and acoustic propagation at sufficiently low excitation levels. One might contrast this to a viscous dashpot, which is also commonly modeled as a linear device. The sliding seals in all viscous dashpots render them essentially-nonlinear from the start. One favorite problem I give year after year, in various forms, is reported here. A generic acoustic transducer, based on a linear simple harmonic oscillator is presented and often the system response function is given in the problem statement. Derivation of the transfer function could be a problem from earlier or later in the class. The students are asked to predict the time domain output of the transducer, subject to a periodic forcing composed of a sawtooth wave, using frequency-domain convolution and Fourier series. Various sub-questions explore the effect of transducer bandwidth and damping on the output signal. A variation of this problem using time-domain convolution is also a favorite. Predictions can be compared to measurements.