A tuning fork when vibrating along with a sonometer produces 6 beats per second when the length of the wire is either 20 cm or 21 cm . Find the frequency of the tuning fork.

Options

A. 226 Hz
B. 246 Hz
C. 236 Hz
D. 256 Hz

Answer

B

Explanation

Let n be the frequency of the tuning fork .
As there are 6 beats/sec, the frequencies of the wire will be `n + 6` for 20 cm length and `n - 6` for 21 cm length of the wire .
` (. :' n propto 1/l)`
For a sonometer wire , ` n_(1) l_(1) = n_(2) l_(2)`
` :. (n + 6) 20 = (n - 6) xx 21 `
` 20n + 120 = 2 1n - 126`
` :. 21n - 20 n = 120 + 126 = 246 ` Hz