Question

A sonometer wire of length `1.5m` is made of steel. The tension in it produces an elastic strain of `1%`. What is the fundamental frequency of steel if density and elasticity of steel are `7.7 xx 10^(3) kg//m^(3)` and `2.2 xx 10^(11) N//m^(2)` respectively ?
A. `188.5 Hz`
B. `178.2 Hz`
C. `200.5 Hz`
D. `770 Hz`

Answer 1

Correct Answer - 2
`f = (v)/(2l) = (1)/(2l)sqrt((T)/(mu)) = (1)/(2l)sqrt((T)/(Ad))`
Also `Y = (Tl)/(ADeltal) rArr (T)/(A) = (YDeltal)/(l) rArr f = (1)/(2l)sqrt((yDeltal)/(ld))`
`l = 1.5m, (Deltal)/(l) = 0.01, d = 7.7 xx 10^(3) kg//m^(3)`
After solving
`f = sqrt((2)/(7)) xx (10^(3))/(3) Hz`.
`f = 178.2 Hz`.