The one-dimensional wave equation was derived with either sound pressure or particle velocity as the dependent variable. Particle displacement, or the variational density, may also be used as the dependent variable. This can be seen from Eqs. (2.4a) and (2.13a) and the conservation of mass, which requires that the product of the density and the volume of a small box of gas remain constant. That is,

${\rho}^{\prime}V={\rho}_{\text{0}}{V}_{\text{0}}=\text{constant}$

(2.28)

and so

${\rho}^{\prime}dV=-Vd{\rho}^{\prime}\text{.}$

(2.29)

Let

${}^{}$

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