Nonlinear waveform steepening in time reversal focusing of airborne, one-dimensional sound waves, and the absence of Mach stems

Abstract

Time reversal (TR) is a process that can be used to generate high amplitude focusing of sound. Previous research has shown that TR in reverberant environments can generate peak levels that exceed 200 dB with airborne, audible sound [Patchett and Anderson, J. Acoust. Soc. Am. 151(6), (2022)], and 134 dB with airborne ultrasound [Wallace and Anderson, J. Acoust. Soc. Am. 150(2), (2021)]. Particularly, in the focusing of audible sound, these high amplitude focused waveforms exhibit multiple nonlinear properties including waveform steepening and a nonlinear increase in compressions due to the generation of free space Mach stems. This study attempts to remove the Mach stems by generating the focus in a 1D system, since Mach stems require higher dimensional spaces to form. The system of pipes used ensures a planar 1D reverberant environment. Results show that waveform steepening remains as expected but that the nonlinear increase in compression amplitudes disappears without the ability for Mach stems to form. This provides further confirmation that Mach stems are the cause of the nonlinear increase in compression amplitudes observed with high amplitude TR.