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Wave Optics

Question
CBSEENPH12039471

A pipe open at both ends has a fundamental frequency f in the air. The pipe is dipped vertically in water so that half of it is in water. The fundamental frequency of the air column is now:

  • f/2

  • 3f/4

  • 2f

  • f

Solution

D.

f

For open ends, fundamental frequency f in air
we have

straight lambda over 2 space equals space straight l
straight lambda space equals space 2 straight l
straight v space equals fλ
straight f equals straight v over straight lambda space equals space fraction numerator straight v over denominator 2 straight l end fraction
When a pipe is dipped vertically in the water, so that half of it is in water, we have

straight lambda over 4 space equals space 1 half
straight lambda space equals space 2 straight l rightwards double arrow space straight v equals space straight f apostrophe straight lambda
straight f apostrophe space equals space straight v over straight lambda space equals fraction numerator straight v over denominator 2 straight l end fraction space equals space straight f
Thus, the fundamental frequency of the air column is now,
f=f'

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