Answer :

The frequency depends on the length L, mass per unit length m and tension F

f LaFbmc

Let us assume a dimensionless constant k such that

f = k LaFbmc

Dimensions of f = [T-1]

Dimensions of L = [L]

Dimensions of F = [MLT-2]

Dimensions of m = [ML-1]


[T-1] = [L]a [MLT-2] b [ML-1]c

= [Mb+c La+b-c T-2b]

On comparing we can see that

b + c =0 …(i)

a + b – c =0 …(ii)

-2b = -1 …(iii)

On solving (i), (ii) and (iii)

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

So frequency can be expressed as

f = k L-1 F1/2 m-1/2

f =

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