A long cylindrical tube carries a highly polished piston and has a side opening . A tuning fork of frequency `n` is sounded at the open end of the tube . The intensity of the sounded heard by the listener changes if the piston is moved in or out. At a particular position of the piston he hears a maximum sound . When the piston is moved through a distance of `9 cm`, the intensity of sound becomes minimum. If the speed of sound is `360 m//s`, the value of `n` is

Options

A. `129.6 Hz`
B. `500 Hz`
C. `1000 Hz`
D. `2000 Hz`

Answer

C

Explanation

When piston moves a distance `x_(1)`, path difference changes by ` 2 x`.
Therefore , the path difference between maxima and consecutive minima ` = lambda//2`
` 2 x = lambda//2`
or `lambda = 4 x = 4 xx 9 cm = 36 cm = 0.36 m`
`n = (v)/(lambda) = (360)/(0.36) = 1000 Hz`