A tuning fork of frequency `340 H_(Z)` is sounded above an organ pipe of length `120 cm` . Water is now slowly poured in it . The minimum height of water column required for resonance is ( speed of sound in air = `340 m//s`)

Options

A. `15 cm`
B. `25 cm`
C. `30 cm`
D. `45 cm`

Answer

D

Explanation

Because the tuning fork is in resonance with air column in the pipe closed at one end, the frequency
is `n=((2N-1)v)/(4l)` where `N=1,2,3` corresponds to different mode of vibration putting `n=340Hz`, `v=340 m//s`, the length of air column in the pipe can be
`l=((2N-1)340)/(4xx340)=((2N-1))/(4)m=((2N-1)xx100)/(4)cm`
For `N=1,2,3` .. we get `l=25cm,75cm,125cm`.. As the tube is only 120 cm long, length of air column after water is poured in it may be 25 cm or 75 cm only, 125 cm is not possible, the corresponding length of water column in the tube will be `(120-25)cm=95cm` or `(120-75)cm=45cm`. Thus minimum length of water column is 45 cm.