Corrections to Morse and Ingard's variational-based treatment of weakly-nonlinear acoustics in lossless gases

What is it about?

Models for sound waves of considerable amplitude (pressure magnitude) must incorporate "nonlinear" or "finite-amplitude" effects. That is to say, the equations of nonlinear acoustics have to be used to account for the change of the sound wave's profile and properties as it propagates through a medium (for example, air). This work concerns the derivation of such nonlinear acoustic equations.

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Why is it important?

In this work, we point out and correct an error in the derivation of finite-amplitude (nonlinear) acoustic wave equations. Specifically, we correct the Lagrangian, given in the classical textbook of Morse and Ingard, from which the nonlinear acoustic wave equation is derived. In doing so, we also show that the resulting corrected governing equation is also consistent with other recent work on the topic.