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Waves question

2023 · Q134
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Waves question

2023 · Q134

NEETPhysicsWavesMCQ+4 / −1

The ratio of frequencies of fundamental harmonic produced by an open pipe to that of closed pipe having the same length is

  1. A
    2:12: 12:1
  2. B
    1:31: 31:3
  3. C
    3:13: 13:1
  4. D
    1:21: 21:2
View written solutionFree

Correct answer: A

The fundamental frequency of an open pipe, noop, is given by V / (2L), where V is the speed of sound and L is the length of the pipe.

For a closed pipe of the same length, the fundamental frequency, ncop, is V / (4L) since only half as many wavelengths fit into the same length due to the closed end.

Therefore, the ratio of frequencies of an open pipe to a closed pipe is:

$$\frac{n_{\text{oop}}}{n_{\text{cop}}} = \frac{V / (2L)}{V / (4L)} = \frac{4L}{2L} = 2:1$$

This shows that the fundamental frequency of an open pipe is twice that of a closed pipe of the same length.

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