A tuning fork of frequency `200 Hz` is in unison with a sonometer wire . How many beats are heard in `30 s` if the tension is increased by `1%` ( in terms of `xx10`]

Answer

`3`

Explanation

`f prop sqrt(T)` for strings.
On increasing the tension by `1 %`
`f' = sqrt(101 T)`
`(f')/(f) = (sqrt(101 T))/(sqrt(T)) = ( 1 + 0.01)^(1/2) = 1 + (1)/(200)`
Beat frequency ,`f' - f = f ((f')/(f) - 1) = 1`
Number of beats in `3 s = 1 xx 30 = 30`