A source of frequency 340 Hz is kept above a vertical cylindrical tube closed at lower end. The length of the tube is 120 cm. Water is slowly poured in just enough to produce resonance. Then, the minimum height (velocity of sound = 340 m/s) of the water level in the tube for that resonance is

Options

A. 0.75 cm
B. 0.25 cm
C. 0.95 cm
D. 0.45 cm

Answer

d

Explanation

The frequency of source `t_(2) = 340` Hz

velocity of sound = 340 m/s
Length of the tube = 120 cm
The minium height of the tube for resonance, `I_(1) = (V)/(4f)`
`= (340)/(4 xx 340) m`
`= (1)/(4) = 0.25 m = 25 cm`
From second resonance condition for closed pipe,
`h = I_(2) - 3I_(1)`
Here, `J_(2) = 120 cm`
`implies h = 120 - 3 xx 25`
`= 120 - 75`
`= 45 cm = 0.45 cm`
so, for second resonance, 0.45 m should be the height of water level. It will be the minimum height of water in the tube