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There are two types of velocities associated with waves:
• Particle velocity
• Wave velocity
The SI unit of velocity is $m/s$.

Particle velocity:
Particle velocity is the rate at which the medium's particles vibrate in order to transfer energy in the form of a wave.

Wave velocity:
The wave velocity is the velocity at which the wave travels through the medium. In other words, the velocity of a sound wave is the distance travelled by a sound wave in one unit of time.
It is mathematically represented as,

$\mathit{Velocity}=\frac{\mathit{Distance}}{\mathit{time}\phantom{\rule{0.147em}{0ex}}\mathit{taken}}$

If one wavelength (λ) represents the distance travelled by one wave and one time period ($$T$$) represents the time taken for this propagation, the expression for velocity can be written as

$v=\frac{\mathrm{\lambda }}{t}$

As a result, the distance travelled by a sound wave per second can be defined as velocity.

We know,

$\begin{array}{l}\mathit{Frequency}\left(n\right)=\frac{1}{T},\\ \mathit{Equation}\phantom{\rule{0.147em}{0ex}}1\phantom{\rule{0.147em}{0ex}}\mathit{can}\phantom{\rule{0.147em}{0ex}}\mathit{be}\phantom{\rule{0.147em}{0ex}}\mathit{written}\phantom{\rule{0.147em}{0ex}}\mathit{as},\\ v=n\mathrm{\lambda }\end{array}$

Solids have the highest sound wave velocity because they are more elastic than liquids and gases. The velocity of sound in a gaseous medium is the lowest because gases are the least elastic.
Therefore,

$\begin{array}{l}{v}_{S}>{v}_{L}>{v}_{G}\\ \mathit{Where},\\ {v}_{S}-\mathit{Velocity}\phantom{\rule{0.147em}{0ex}}\mathit{of}\phantom{\rule{0.147em}{0ex}}\mathit{sound}\phantom{\rule{0.147em}{0ex}}\mathit{in}\phantom{\rule{0.147em}{0ex}}\mathit{solids}\\ {v}_{L}-\mathit{Velocity}\phantom{\rule{0.147em}{0ex}}\mathit{of}\phantom{\rule{0.147em}{0ex}}\mathit{sound}\phantom{\rule{0.147em}{0ex}}\mathit{in}\phantom{\rule{0.147em}{0ex}}\mathit{liquids}\\ {v}_{G}-\mathit{Velocity}\phantom{\rule{0.147em}{0ex}}\mathit{of}\phantom{\rule{0.147em}{0ex}}\mathit{sound}\phantom{\rule{0.147em}{0ex}}\mathit{in}\phantom{\rule{0.147em}{0ex}}\mathit{gases}\end{array}$