A tuning fork vibrating with a sonometer having 20 cm wire produces 5 beats per second. The beat frequency does not change if the length of the wire is changed to 21 cm. The frequency of the tuning fork (in Hertz) must be

Options

A. 205
B. 215
C. 210
D. 200

Answer

A

Explanation

Let N be the frequecy of the tuning fork .
There are 5 beats/sec, when the length of the wire is 20 cm and when the length is increased from 20 cm to 21 cm , there are 5 beats/s and since ` n propto 1/L`.
` :. ` The frequency of the wire for ` L_(1) = 20 cm " is " N + 5 " and for " L_(2) = 21 ` cm, the frequency of the wire will be N - 5.
Thus we get 5 beats/sec. in both cases .
`:. n_(1) L_(1) = n_(2) L_(2) " where " n_(1) = N + 5 " and " N_(2) = N - 5`
` :. (N + 5) xx 20 = (N - 5) xx 21 `
` :. 20 N + 100 = 2 1N - 105`
` :. 21N -20N = 105 + 100 = 205`
` :. N = 205` Hz