On the Measurement of Shock Waves

Abstract

The classic theoretical formulations of finite-amplitude distortion invariably depict continuous sinusoidal waves which develop into sawtooth or N-shaped waves. In practice, where ultrasonic wave- forms at high intensities are measured by a PVDF hydrophone con- nected to an oscilloscope, waveforms are observed with gross asym- metries between positive and negative pressure amplitudes, high- amplitude spikes, notches, ringing, and other peculiarities. In princi- ple, additional nonlinearities in the driving stages or the receiving sys- tem may influence the observed waveform. However, it is not necessary to invoke nonlinearities in the transmit or receive systems to explain the time-domain appearance of many waveforms. Instead, linear mechanisms exist which affect the waveshape. The first is a relative phase shift betwen the fundamental and second (and higher) harmonics which occurs in a diffraction-limited focused field. This alters the time- domain appearance but not the spectral content of the observed signal. The second class of linear mechanisms involves hydrophone cable and impedance mismatch effects which alter both time- and frequency-do- main characteristics of the actual pressure waveform incident on the hydrophone. These effects and others are illustrated. The results form the basis for some recommendations on experimental procedures in nonlinear wave propagation.