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 ?

Options

A. `188.5Hz`
B. `178.2Hz`
C. `200.5Hz`
D. `770Hz`

Answer

B

Explanation

Here,`l=1.5m, (DeltaL)/(L)=1%, n=?`
`rho=7.7xx10^(3)kg//m^(3)` and `Y=2.2xx10^(11)N//m^(2)`
From `Y=(F)/(A(DeltaL//L))`
`F=YA((DeltaL)/(L))=2.2xx1^(11)Axx(1)/(100)=2.2Axx10^(9)`
From `v=(1)/(2l)sqrt((T)/(m))`
`v=(1)/(2l)sqrt((F)/(Axx1xxrho))=(1)/(2xx1.5)sqrt((2.2xx10^(9)A)/(Axx7.7xx10^(3)))`
`v=(10^(3))/(3)sqrt((2)/(7))=178.Hz`