A string oscillating at fundamental frequency under a tension of 225 N produces 6 beats/sec with a fork . If the tension is increased to 256 N, then again oscilaating at its fundamental note it produces 6 beats/sec, with the same fork . What is the frequency of the tuning fork ?

Options

A. 186 Hz
B. 225 Hz
C. 250 Hz
D. 300 Hz

Answer

A

Explanation

For the vibrating string ,
`n = 1/(2L) sqrt(T/m) " " :. n_(1)/n_(2) = T_(1)/T_(2) = sqrt((225)/(256)) = 15/16`
` :. n_(1) lt n_(2) `
Let N be the frequency of the tuning fork .
In both cases, we get 6 beats/sec.
` :. n_(1) = N - 6 " and " n_(2) = N + 6 `
` :. (N - 6)/(N+6) = 15/16`
` :. 16 N - 96 = 15 N + 90 " " :. N = 96 + 90 = 186 ` Hz