Speed of sound wave in medium on depends modulus of elasticity and density of medium, then find a relation for speed of sound wave(in terms of given parameters).

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Solution

Elastic density of medium = $d = m a s s / l e n g t h = M L^{-} 3$

Coefficient of elasticity $E = s t r e s s / s t r a i n$ = $M L^{- 1} T^{- 2}$

let velocity $v$ be = $d^{n} \times E^{m}$

so $L^{1} T^{- 1} = M^{(n + m)} \times L^{(- 3 n - m)} \times T^{(- 2 m)}$

equating the powers of corresponding dimensions
$n + m = 0$ so $n = - m$

$3 n + m = - 1$ => $n = \frac{- 1}{2} a n d m = \frac{1}{2}$

So the formula is : $v = K \sqrt{\frac{E}{d}}$ where $K$ is a constant

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