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. 45 cm
B. 30 cm
C. 35 cm
D. 25 cm

Answer

A

Explanation

Using relation `v=v lambda`
`or lambda=(v)/(nu) =(340)/(340)=1m`
If length of resonance columns are `l_(1),l_(2) and l_(3),` then
`l_(1)=(lambda)/(4)=(1)/(4)m=25cm " " `(for first resonance)
`l_(2)=(3lambda)/(4)=75cm " " `(for second resonance)
`l_(3)=(5lambda)/(4)=125 cm " " ` (for third resonances)
This case of third resonance is impossible because total lwngth of the tube is 120 cm.
So, minimum height of water
`120-75=45 cm `