Nonlinear waveform steepening in time reversal focusing of airborne, one-dimensional sound waves

Time reversal (TR) is a process that can be used to generate high amplitude focusing of sound. It has been previously shown that high amplitude focused sound using TR in reverberant environments exhibits multiple nonlinear features including waveform steepening and a nonlinear increase in peak compression pressures [Patchett and Anderson, J. Acoust. Soc. Am. 151(6), 3603-3614 (2022)]. The present study investigates the removal of one possible cause for these phenomena: free-space Mach stems. By constraining the focusing in the system to one-dimensional (1-D) waves, the potential formation of Mach stems is eliminated so that remaining nonlinear effects can be observed. A system of pipes is used to restrict the focused waves to be planar in a 1-D reverberant environment. Results show that waveform steepening effects remain, as expected, but that the nonlinear increase in compression amplitudes that appears in TR focusing of three-dimensional (3-D), finite-amplitude sound in rooms disappears here because Mach stems cannot form in a 1-D system. These experiments do not prove that Mach stems cause the nonlinear increase observed for focusing in a 3-D environment, but they do support the Mach stem explanation.