A vibrating string of certain length l under a tension T resonates with a mode corresponding to the first overtone (third harmonic) of an air column of length 75 cm inside a tube closed at one end. The string also generates 4 beats per second when excited along with a tuning fork of frequency n. Now when the tension of the string is slightly increased, the number of beats reduces to 2 per second. Assuming the velocity of sound in air to be 340 m/s, the frequency n of the tuning fork in Hz is

Options

A. `344`
B. `336`
C. `117.3`
D. `109.3`

Answer

A

Explanation

As string and tube are in resonance `f_(1) = f_(2)`
`|f_(1) - n| = 4 Hz`.
When `T` increase, `f_(1)` also increases. It is given that beat frequency decreases to `2 Hz`.
`rArr n - f_(1) = 4`
`n = 4 + f_(1)`
as `f_(1) = f_(2)`
`n = 4 + f_(2)`

`n = (4 + f_(2))`
`f_(2) = (3V)/(4l) = (3 xx 340)/(4 xx (3//4)) = 340`
`n = 344`