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A sonometer wire vibrates with frequency...

A sonometer wire vibrates with frequency `n_(1)` in air under a suitable load of specific gravity `'sigma'` . What the load is immersed in water , the frequency of vibration of wire `(n_(2))` will be

A

`n_(1) sqrt((sigma +1)/sigma)`

B

`n_(1) sqrt((sigma - 1)/sigma)`

C

`n_(1) sqrt(sigma/(sigma + 1)) `

D

`n_(1) sqrt(sigma/(sigma - 1))`

Text Solution

Verified by Experts

The correct Answer is:
B
For sonometer wire , `n = 1/(2L) sqrt(T/m) = 1/(2L) sqrt((Mg)/m) `
where tension T = Load Mg
= Volume (V) ` xx " density " ( sigma) xx g`
` :. N_(1) = 1/(2L) sqrt((V sigma g)/m)` …(1)
When the load is dipped in water , the apparent weight
= Real weight - Loss of weight in water
` V sigma g - V xx 1 xx g = V_(g) ( sigma - 1) `
` :. n_(2) = 1/(2L) sqrt((V ( sigma - 1)g)/m) ` ....(2)
` :. n_(2)/n_(1) = sqrt((sigma - 1)/sigma)`
`n_(2) = n_(1) sqrt((sigma - 1)/sigma) ` ....(3)
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