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A sonometre wire of length 1.5 m is made...

A sonometre wire of length 1.5 m 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

178.2 Hz

B

200.5 Hz

C

770 Hz

D

188.5 Hz

Text Solution

Verified by Experts

The correct Answer is:
A
Fundamental frequency , f = `(1)/(2l ) sqrt((T)/(mu))`
= `(1)/(2l ) sqrt((T)/(A rho ))`
` (1)/(2l ) sqrt(("Stress")/(rho))`
` (1)/(2l ) sqrt((Y xx "Strain")/(rho)) `
` = (1)/(2xx 1.5) sqrt( (2.2 xx 10^(11) xx 10^(-2))/(7.7 xx 10^(3)))`
= 178.2 Hz
So, Correct choice is a.
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