Finite amplitude standing waves in harmonic and anharmonic tubes

Abstract

Finite amplitude standing waves have been studied in closed tubes filled with air and driven by a piston at frequencies near 200 Hz. The tubes were driven at resonance generating standing waves with amplitudes of up to 160 dB re: 20 μPa. The main objective was to measure the dissipation of energy by the fundamental frequency and the higher harmonics, as well as by other nonacoustic mechanisms. A formulation developed by Coppens and Sanders [J. Acoust. Soc. Am. 58, 1133–1140 (1975)] using a single nonlinear equation to describe standing waves in cavities of arbitrary resonance frequencies and quality factors was used successfully to predict the higher harmonics. In addition, the effect of detuning the tubes on the energy dissipation was measured in tubes with variable cross sections. It was found that the detuned tubes effectively suppress the energy transfer into (and energy dissipation by) the higher harmonics. It was also found that expanding rather than contracting the cross section of the tubes minimized the dissipation of energy through nonacoustic mechanisms.