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An organ pipe of length L open at both ends is found to vibrate in its first harmonic when sounded with a tuning fork of 480 Hz. What should be the length of a pipe closed at one end, so that it also vibrates in its first harmonic with the same tuning fork?
An organ pipe of length L open at both ends is found to vibrate in its first harmonic when sounded with a tuning fork of 480 Hz. What should be the length of a pipe closed at one end, so that it also vibrates in its first harmonic with the same tuning fork?
CBSE | Class 11 | NCERT Exemplar | Physics | Waves
An organ pipe of length L open at both ends is found to vibrate in its first harmonic when sounded with a tuning fork of 480 Hz. What should be the length of a pipe closed at one end, so that it also vibrates in its first harmonic with the same tuning fork?

Answer:

Because the medium, frequency, and number of harmonics are the same in open and closed pipes, the number of nodes and (wave) will be the same in both circumstances.

When the harmonic is open, we have:

L = λ/2

Or, λ = 2L

We can write: v/f0 = 2L

(f0)open = v/2L

where v denotes the speed of the sound wave in the air.

Similarly, when the harmonic is closed, we have

L’ = λ/4

Or, λ = 4L’

(f0)closed = v/4L’

v/2L = v/4L’

L’ = L/2

For a resonant first harmonic with the same frequency, the length of one end closed pipe will be half that of both ends open pipe.

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