Plane Sound Waves of Finite Amplitude in a Non-Dissipative Medium

摘要

A theoretical treatment of plane progressive sound waves of finite amplitude in a non-dissipative medium produced by a piston whose motion contains many different frequency components is presented herein. The solution of the second-order wave equation is represented in the form of a Fourier series and the coefficients are expressed in terms of Bessel functions. The progressive distortion of the wave form and the generation of higher harmonics are studied from consideration of the energy density of the different frequency components. Due to the non-linearity between the pressure and specific volume, there is found to be a transfer of energy from components of lower frequency to those of higher frequency. This transfer of energy is more efficient if harmonics are initially present in the sound wave. (Author)