Question

Check the accuracy of the relation v = 1/2l √T/m, where v is the frequency, l is the length, T is the tension and m is mass of unit length of the string.

Answer 1

v = 1/2l √T/m

Write the dimensions on either sides, we have

L.H.S. = v =[T^-1] = [M⁰L⁰T^-1]

R.H.S. = 1/2l = √T/m

(As 1/2 has no dimensions)

Tension is force and m is mass per unit length,so

As, L.H.S. = R.H.S., dimensionally. therefore, formulae is correct.