Question

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).

Answer 1

Elastic density of medium = $d=mass/length=ML{}^{-}3$

Coefficient of elasticity $E=stress/strain$ = $M{L}^{-1}{T}^{-2}$

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

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

equating the powers of corresponding dimensions

$n+m=0$ so $n=-m$

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

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