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The velocity of sound depends upon elastic density of medium and coefficient of elasticity .derive expression by dimensional analysis.




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Elastic density of medium = d  = mass / length  = M L⁻³

Coefficient of elasticity E = stress / strain
           =  [ M L⁻¹ T⁻²   ]

let velocity v  be =  d^n    E^m

     so  L¹ T⁻¹  =  M^(n+m)   L^(- 3 n - m )  T^(- 2m)

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

                3 n + m = -1         =>   n = -1/2  and  m = 1/2

SO the formula  is :    v  = K √ (E / d)          where  K is a constant

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