When a tuning fork vibrates with `1.0 m` or `1.05 m` long wire of a , `5` beats per second are produced in each case. If the frequency of the tuning fork is `5f` (in `Hz`) find `f`.

Answer

41

Explanation

Let frequency tuning fork `= f`
frequency of wave in wire `= (v)/(2l)`
when `l = 1 m`
`f_(1) = (v)/(2)`
when `l = 1.05m`
`f_(2) = (v)/(2 xx (1.05))`
`f_(1) - f = 5` , and `f - f_(2) = 5 rArr f_(1) - f_(2) = 10`
`rArr (v)/(2)(1 - (1)/(1.05)) = 10` or `v = (20 xx 1.05)/(0.05) = 420 m//s`.
`f_(1) = (v)/(2) = 210 Hz`.
`f = f_(1) - 5 = 205 Hz`.