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Wave Optics

Question
CBSEENPH12039527

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

  • f

  • f/2

  • 3f/4

  • 2f

Solution

A.

f

Initially for open organ pipe, fundamental frequency,
straight v subscript straight o space equals space fraction numerator straight v over denominator 2 l end fraction space equals straight f
But when it is half dipped in water, then it becomes closed organ pipe of length l/2. In this case fundamental frequency.
straight v subscript straight c space equals space fraction numerator straight v over denominator 4 l end fraction space equals space fraction numerator straight v over denominator 4 begin display style l over 2 end style end fraction space equals space fraction numerator straight V over denominator 2 l end fraction space equals straight f

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