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PhysicsNEET 2025Superposition, standing waves, beats

Waves

A pipe open at both ends has a fundamental frequency ff in air. The pipe is now dipped vertically in a water drum to half of its length. The fundamental frequency of the air column is now equal to:

  1. A.f2\dfrac{f}{2}
  2. B.ff✓
  3. C.3f2\dfrac{3f}{2}
  4. D.2f2f

Solution

Open pipe of length LL: f=v2Lf = \frac{v}{2L}. Dipped to half its length it becomes a closed pipe of length L2\frac{L}{2}: f′=v4(L/2)=v2L=ff' = \frac{v}{4(L/2)} = \frac{v}{2L} = f.

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