Question

A sonometer wire of length 0.5 m is stretched by a weight of 5 kg. The fundamental frequency of vibration is 100 Hz. Calculate linear density of wire.

Answer 1

Given : L= 0.5 m, T = 5kg = 5 x 9.8 = 49N, n = 100 Hz

n = \(\frac{1}{2L}\sqrt{\frac{T}{m}}\)

∴ Linear density, m = \(\frac{T}{4L^2n^2}\) = \(\frac{49}{4(0.5)^2(100)^2}\)= 4.9 x 10⁻³ kg/m