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?

Options

A. `0.01`
B. `0.02`
C. `0.03`
D. `0.04`

Answer

B

Explanation

`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`