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Question

In a long cylindrical tube the wave level is adjusted and the air column above it is made to vibrate in unison with a vibrating tuning fork kept at the open end. Maximum sound is heard when the air column lengths are equal to


A
λ4 , 3λ4
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B
λ2 , 3λ2
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C
λ,3λ
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D
λ , 3λ4
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Solution

The correct option is A $$\dfrac{\lambda}{4} $$ , $$\dfrac{3\lambda}{4} $$
So in general the formula for the resonance length will be:
$$\displaystyle \frac{(2n-1)\lambda}{4}$$, where $$n=1, 2, 3$$..
First booming sound indicates that at that length, $$l_1$$, of an air column in organ pipes with one end closed is in resonance with the given frequency.
And that length is,
$$l_1= \lambda /4$$
The next resonance length will be :
$$l_2=3\lambda/4$$

Physics

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