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A string is under tension so that its le...

A string is under tension so that its length is increased by `1//n` times its original length . The ratio of fundamental frequency of longitudinal vibrations and transverse vibrations will be

A

`eta :1`

B

`1:eta`

C

`sqrt eta :1 `

D

`1: sqrt eta`

Text Solution

Verified by Experts

The correct Answer is:
D
Tension in the string will be given by
`T = ((YADeltal)/l) = (YA)/eta` (as `(Deltal)/l = 1/eta)`
Now, `f prop v`
`f_1/f_2 = v_1/v_2 = sqrt(T//(rhoA))/sqrt(T//rho)`
`= sqrt (T/(YA)) = 1/ sqrt(eta).`
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