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Apparently, in the case of transverse waves, its velocity depends only on the properties of the medium, it doesn't depend on its source (see this question).

I was wondering: is the same also true for longitudinal waves (sound waves, for example)?

Intuitively, one would think its velocity should also depend on its source (how "hard" it hits the medium in front of it, for example).

Which is true? Does the speed of longitudinal waves also depend only on the properties of the medium?

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The longitudinal and transverse velocity of waves are defined as follows: \begin{align} v_{\rm L}=\sqrt{\frac{E(1-\mu)}{\rho(1+\mu)(1-2\mu)}}&\stackrel{\mu=0}{=}\sqrt{\frac{E}{\rho}},\\ v_{\rm T}&=\sqrt{\frac{G}{\rho}}. \end{align} Where $\mu$ is the Poisson's ratio, $E$ is the modulus of elasticity, $G=\frac{E}{2(1+\mu)}$ is the shear modulus and $\rho=\frac{m}{A\cdot dx}$ is the density of the propagation material.

You can find a derivation in german on pages 16-20 of this pdf.

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