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Elastic Waves. Acoustics.

Problem 4.153

A plane elastic wave \(\xi=a \cos (\omega t-k x)\) propagates in a medium \(K\). Find the equation of this wave in a reference frame \(K^{\prime}\) moving in the positive direction of the \(x\) axis with a constant velocity \(V\) relative to the medium \(K .\) Investigate the expression obtained.

Reveal Answer
ξ=acos⁡[(1−V/v)ωt−kx′], where v=ω/k\xi=a \cos \left[(1-V / v) \omega t-k x^{\prime}\right], \text { where } v=\omega / k
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