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Derive an expression for the velocity of sound in a material medium, assuming the temperature of the medium to be constant.

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The velocity of sound v may depend upon (i) the density (d) of the medium and (ii) the elasticity (E) of the medium. Hence, we can write

v α Ea db or, K Ea db.

Writing the dimensions of different quantities in above equation, we get

or, [M0LT-1] = [ML-1T-2]a [ML-3 T0]b

[M0LT-1] = Ma+b L-a-3b T-2a

Equating the powers of the like quantities, we obtain, a+b = 0

-a -b = 1

-2a = -1

Solving these equations, we get

a = 1/2 and b = -1/2

Hence, v = K.E1/2 d-12 or, v = K √E/d.

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