Waves in elastic media
In longitudinal waves, the displacement of the medium is $||$ direction
of wave propagation; in transverse waves it is $\perp$
Velocity $v$, period $T$, wavelength $\lambda$ of the wave
\[
v = {\lambda\over T} = \lambda f
\]
Velocity of transverse waves on a string
\[
v = \sqrt{\frac{F}{m/l}} \qquad \frac{m}{l} - \mbox{linear density}
\]
Velocity of longitudinal sound waves in
\begin{eqnarray*}
\mbox{long solid bars} & & v=\sqrt{\frac{\cal Y}{\rho}} \qquad {\cal Y} - \mbox{Young's modulus}\\
\mbox{liquids} & & v=\sqrt{\frac{\cal B}{\rho}} \qquad {\cal B} - \mbox{bulk modulus}\\
\mbox{ideal gases} & & v=\sqrt{\frac{\gamma k T}{m}} \qquad \gamma=\frac{C_p}{C_v}, \> T - \mbox{temperature}
\end{eqnarray*}
In general, $v_{\rm solids} > v_{\rm liquids} > v_{\rm gases}$
Longitudinal and transverse waves may have different velocities in the same medium
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