The length of the wire shown in figure between the pulley is 1.5 m and its mass is 12.0 g. Find the frequency of vibration with which the wire vibrates in two loops leaving the middle point of the wire between the pulleys at rest.

Explanation

Tension in wire
`T=9 kg wt =9 g=9xx9.8`
Mass per unit length `m M//L`
`=(12xx10^(-3) kg)/(1.5 m)=8xx10^(-3) kg//m`
`:.` Frequency of vibration of pth harmonic on string
`n=(p)/(2l) sqrt(T/m)=(2)/(2xx1.5) sqrt({(9xx9.8)/(8xx10^(-3))})=70 Hz`