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

A sonometer 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

`188.5 Hz`

B

`178.2 Hz`

C

`200.5 Hz`

D

`770 Hz`

Text Solution

Verified by Experts

The correct Answer is:
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`.
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