Elastic waves in solids can be coupled with both the electrical and magnetic potentials, the speed of light is five orders larger than the speed of elastic waves.
Aleksey, I don't quite understand what your qusetion is about. If you ask for proof of the approximations, well, you have already given it. The main reason for the approximations to be valid is the fact that the speed of sound is much less than that of light. So, when one writes the corresponding Maxwell equations, the time-dependent terms are omitted. If you are curious about the equations see, for example, the classic book
Auld B.A. Acoustic Fields and Waves in Solids. New York: John Wiley & Sons, 1973.
Anton, thank You for Your answer. Indeed, I have read the book by Auld. I asked this question because this month I had an attempt to take a PhD here in Krasnoyarsk at the Siberian State Aerospace University and this problem was the main for the head of VAK (Vsshaya Attestationnaya Komissiya) Prof. S.I. Senashov and for the head of Kafedra of Physics Prof. S.S. Aplesnin who believes that the time-dependent terms should be in the equations for which I have found solutions , namely discovered by about halfhundred new waves!!!! As a result, I have still no PhD because Prof. Senashov said me that I have no publications on Mechanics and I have to write and publish three new publications and publish them in Mechanics, namely I have to write a new PhD anew!!!! I have to state that I have published 27 papers in International Journals and 5 books. I understand that they will require more and more from me as soon as i will satisfy their requirements for the PhD and i will have no PhD.
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