of acoustic energy conservation

Here, So is the internal energy. The quantities Po, Qo, Vo and So characterize both the ambient state of an inhomogeneous moving medium and sound vibrations propagating in that medium. Let Po = P + P + P2 + ... , Qo = Q + 17 + 172 + ... , Vo = V+W+W2+'" and So = S+SI +S2+···. Here, P, Q, v and S characterize the ambient state of the medium. In the linear theory p, 17, W and SI characterize a wave propagating in a medium and obey equations (2.8}--(2.12); P2 "" p2, 172 "" 172, W2 "" w2 and S2 "" si. The most consistent method for deriving the law of acoustic energy conservation would be to subtract from equation (3.20) the equality

which expresses the law of energy conservation of the ambient state of the medium, and then to neglect terms of the order of p3, 173 , w 3 and sf. But the resulting equation would contain not only the quantities p, 17 and w characterizing a sound wave, but also the quantities P2, 172, W2 and S2, which are not considered in linear acoustics.