A string of length `50 cm` and mass `12.5 g` is fixed at both ends. A pipe closed at one end has a length `85 cm`. When the string vibrates in its second overtone and the air column in the pipe in its first. Overtone, they produce a beats frquency of `6 Hz`. It is also observed that decreasing teh tension in the string decreaes beats frequency. Neglect the end correction in the pipe and velocity of sound in air is `340 m//s`. then the tension in the string is

Options

A. `72 N`
B. `52 N`
C. `26 N`
D. `18 N`

Answer

B

Explanation

The frequency of vibration of air column in th pipe is `f_(1) = (3v)/(4l) = (3 xx 340)/(4 xx 0.85) = 300 Hz`.
The frequency of vibration of string is `f_(2) = f_(1) + 6 = 300 + 6 = 306 Hz`
Now `f_(2) = (3)/(2l) sqrt((F)/(mu))`
`306 = (3)/(2 xx 0.5) sqrt((F xx 0.5)/(2.5 xx 10^(-3)))`
`306 = 30 sqrt2F`
sqrt2F = 10.2 :. F= 52 N`