Plane sound waves of finite amplitude in a non-dissipative medium
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Abstract
A theoretieal treatment of plane progressive sound waves of finite amplitude in a non-dissipative medium produced by a piston whose motion contains many different frequeney components is presented herein. The solution of the seeond-order wave equation is represented in the form of a Fourier series and the eoeffieients are expressed in terms of Bessel funetions. The progressive distortion of the wave form and the generation of higher harmonies are studied from eonsideration of the energy density of the different frequeney components. Due to the non-linearity between the pressure and speeifie volume, there is found to be a transfer of energy from components of lower frequency to those of higher frequeney. This transfer of energy is more efficient if harmonies are initially present in the sound wave.