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Question
The fundamental frequency of a vibrating organ pipe is 200 Hz.
(a) The first overtone is 400 Hz.
(b) The first overtone may be 400 Hz.
(c) The first overtone may be 600 Hz.
(d) 600 Hz is an overtone.
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Solution
(b) The first overtone may be 400 Hz.
(c) The first overtone may be 600 Hz.
(d) 600 Hz is an overtone.
For an open organ pipe: \[\nu_n = n \nu_1\]
nth harmonic = (n – 1)th overtone
\[\nu_1 = 200 Hz, \nu_2 = 400 Hz, \nu_3 = 600 Hz\]
If the pipe is an open organ pipe, then the 1st overtone is 400 Hz. Option (b) is correct.
Also, υ3 = 600 Hz, i.e., second overtone = 600 Hz.
600 Hz is an overtone. Therefore, option (d) is correct.
If the pipe is a closed organ pipe, then
\[\nu_n = \left( 2n - 1 \right) \nu_1\]
(2n – 1)th harmonic = (n – 1)th overtone
For n = 2:
1st overtone = 3rd harmonic = 3υ1
=3 × 200
= 600 Hz
Therefore, option (c) is also correct.
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