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.