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Question

A tuning fork of frequency 340 Hz is vibrated just above a cylindrical tube of length 120 cm. Water is slowly poured in the tube. If the speed of sound is 340 m/s then the minimum height of water required for resonance is :

A
95 cm
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B
75 cm
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C
45 cm
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D
25 cm
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Solution

The correct option is C 45 cm
The wavelength of the wave is
λ=vν
λ=340340=1m
Therefore for different resonances, the required lengths of the air column are

λ4, 3λ4, 5λ4 i.e. 25cm,75cm,125cm.
As the length of pipe is120cm, the resonance corresponding to 125cm is not possible.
So, when the water is slowly poured, the first resonance will occur at length

75cm of air column. Hence, the height of water is
h=12075=45cm.

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