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Q)

If the velocity of the sound in a gas depends on its bulk modulus of B and

If the velocity of the sound in a gas depends on its bulk modulus of B and it's density P derive the relation of velocity of sound by method of dimension

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A)
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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