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Waves
Organ Pipes and Standing Waves in Air Columns
1 question from 1 paper, each with its answer.
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Concepts tested
- Open and Closed Organ Pipes
All Questions
2025 1 question
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A pipe open at both ends has a fundamental frequency $f$ 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:
Initial open pipe has fundamental $f = \frac{v}{2L}$. Half-submerged pipe is closed at one end of length $L/2$, giving fundamental $f' = \frac{v}{4(L/2)} = \frac{v}{2L} = f$.
For an open organ pipe of length $L$, the fundamental frequency is $f = \frac{v}{2L}$. When the pipe is immersed to half of its length in water, the air column length becomes $L' = L/2$, with the water surface acting as a rigid closed end (closed organ pipe). The fundamental frequency of a closed pipe of length $L'$ is $f' = \frac{v}{4 L'} = \frac{v}{4 (L/2)} = \frac{v}{2L} = f$. Therefore, the fundamental frequency remains unchanged and is equal to $f$.