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Two identical piano wires kept under the...

Two identical piano wires kept under the same tension T have a fundamental frequency of 600 Hz. The fractional increase in the tension of one of the wires which will lead to occurrence of 6 beats/s when both the wires oscillate together would be ......

A

`0.02`

B

`0.03`

C

`0.04`

D

`0.01`

Text Solution

Verified by Experts

The correct Answer is:
A
We have `f = (1)/(2L) sqrt ((T)/( mu )) implies f prop sqrtT implies f = K sqrtT`
(Where K = constant of proporationaly)
`therefore ( df )/( dT) =K (1)/( 2 sqrtT) = (f)/( sqrtT) xx (1)/( 2 sqrtT) = (f)/( 2T)`
`therefore (dT)/(T) =2 ((df)/(f)) =2 xx (6)/( 600) =0.02`
`implies ` Fractional increases in tension `=0.02`
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