Two identical sonometer wires have a fundamental frequency of `500 Hz` when kept under the same tension . The percentage change in tension of one of the wires that would cause an occurrence of `5 beats//s` , when both wires vibrate together is

Explanation

The fundamental frequency of wire is given as
`n_(0) = (1)/(2L)sqrt((T)/(mu))`
On increasing tension by `DeltaT` the new frequency will be
`n_(0)^(') = (1)/(2L)sqrt((T + DeltaT)/(mu))`
`n_(0) sqrt(1+(DeltaT)/(T))`
`n_(0) sqrt(1+(DeltaT)/(2T))`
Now the fractional change in frequency will be
`(n_(0)^(') - n_(0))/(n_(0)) = (1)/(2) (DeltaT)/(T)`
`(DeltaT)/(T) = 2 xx (5)/(500)`
= 0.02