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]


Dimensionally


[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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