The frequency of

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

f L^aF^bm^c

Let us assume a dimensionless constant k such that

f = k L^aF^bm^c

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

= [M^b+c L^a+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 F^1/2 m^-1/2

f =