An open pipe of length ` 2m` is dipped in water . To what depth ` x` is to be immersed in water so that it may resonate with a tuning fork of frequency `170 Hz` when vibrating in its overtone . Speed of sound in air is `340 m//s`

Options

A. `0.5 m`
B. `0.75 m`
C. `1 m`
D. `1.5 m`

Answer

A

Explanation

Length of open organ pipe `l = 2 m`.
When it is dipped in water , it becomes closed at one end . Let `l_(1)` be the length of air column of pipe immersed , then frequency of first overtone of pipe
` = ( 3v)/( 4 l_(1))`
Given `( 3v)/( 4 l_(1)) = 170`
`l_(1) = ( 3v)/( 4 xx 170) = 1.5 m`
Length immersed
`x = l - l_(1)`
`= 2 - 1.5 = 0.5 m`