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.

Answer 1

(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: \[\nu_n  = n \nu_1\] 

n^th 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 1^st 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:
1^st overtone = 3^rd harmonic = 3υ₁
                                           =3 × 200
                                           = 600 Hz
Therefore, option (c) is also correct.