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Two identical piano wires have fundement...

Two identical piano wires have fundemental frequency of `600` `vib//sec`, when kept under the same tension. What frectional increase in the tension of one wire will lead to the occurrence of six beats per second when both wires vibrate simuitaneously?

A

`0.01`

B

`0.02`

C

`0.03`

D

`0.04`

Text Solution

Verified by Experts

The correct Answer is:
B
`f_("beat")=f_(1)-f_(2)`
`implies 6=(1)/(2l)sqrt((T)/(mu))-(1)/(2l)sqrt((T)/(mu))`
`implies (1)/(2l)sqrt((T)/(mu))=606` = fundamental frequency
If `f_(1)=606`, then `f_(2)=f_(1)-f_("beat")=606-6=600`
`(f_(1))/(f_(2))=((1)/(2l)sqrt((T)/(mu)))/((1)/(2l)sqrt((T)/(mu//)))impliessqrt((T.)/(T))=(606)/(600)=1.01`
`implies (T.)/(T)=(1.01)^(2)~~1.02`
`implies (DeltaT.)/(T)=0.02`
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