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Question

In a resonance column experiment, a tuning fork of frequency 850 Hz is used. The first resonance is observed when the air column has a length of 9 cm and the second resonance is observed when the air column has a length of 29 cm. The pressure node is formed at distance X above the open end. Then, value of X is

A
0.5 cm
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B
1 cm
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C
2 cm
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D
4 cm
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Solution

The correct option is B 1 cm
Given that,

First resonance is observed when l1=9 cm

Second resonance is observed when l2=29 cm

Frequency of fork, f=850 Hz


Assume that d is the distance between the top of the column and the pressure node and λ is the wavelength of the wave.

From resonance column experiment
l1+e=λ4 ...(i) (for first resonance)

l2+e=3λ4 ...(ii) (for second resonance)

l2l1=λ2 [from equation (i) & (ii)]

λ=2(l2l1)=2(299)=40 cm

Substituting the value of λ in equation (i),
9+e=404=10e=1 cm
e=X=1 cm

So, pressure node is formed at 1 cm above the open end.

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