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