A tuning fork produces 4 beats /sec, with a sonometer wire of length 40 cm. It is found that when the length is increased to 44 cm, by keeping other factors constant, again 4 beats/sec are produced. What is the frequency of the tuning fork ?

Options

A. 44 Hz
B. 84 Hz
C. 100 Hz
D. 176 Hz

Answer

B

Explanation

Let n be frequency of the tuning fork and `n_(1)` , be the frequency of the wire .
`n_(1)/n_(2) = l_(2)/l_(2) = 44/40 = 11/10 :. n_(1) gt n_(2)`
` :. ` The initial frequency of the wire is more than the frequency of the tuning fork and then it is less .
` :. ( n + 4)/( n- 4) = 11/ 10 :. 11n - 44 = 10 n = 40 `
` :. n = 84 ` Hz