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Question

A tuning fork of frequency 340 Hz is vibrated just above the tube of 120 cm height. Water is poured slowly in the tube. What is the minimum height of water necessary for the resonance?
(speed of sound in air = 340 m/s)

A
45 cm
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B
30 cm
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C
40 cm
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D
25 cm
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Solution

The correct option is A 45 cm
We have

v=fλ.

orλ=vf=340 m/s340 Hz=1 m

First resonating length,

l1=λ4=14 m=25 cm

Second resonating length,

l2=3λ4=3×1 m4=75 cm.

Third resonating length,

l3=5λ4=5×1 m4=125 cm.

So third resonance is not possible since the length of the tube is 120 cm.

Minimum height of water necessary for resonance = 12075=45 cm.

Why this question?

For tube closed at one end the resonance occurs when the tube length is (2n+1)λ4 where n take values 0,1,2....etc


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