Question

Assuming that velocity of sound depend upon elasticity and the density of the medium.
Drive relation between them using dimensional analysis.
Using prinsinle of homogeneity of dimensions drive the relation for the time period of a​

Answer 1

Answer:

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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