Question

Two nearest harmonics of an organ pipe open at both the ends are 200Hz and 240Hz. The fundamental frequency

Answer 1

Answer:

Frequency of mth harmonic in an open organ pipe ν

m

=

2L

mv

Fundamental frequency in an open organ pipe i.e m=1 ν

1

=

2L

v

Frequency of nth harmonic in a closed organ pipe ν

n

′

=

4L

nv

Frequency of 3rd harmonic in a closed organ pipe ν

3

′

=

4L

3v

Now ν

3

′

−ν

1

=100

Answer 2

The fundamental frequency is 40 Hz.

Given: Two nearest harmonics of an organ pipe open at both the ends are 200 Hz and 240 Hz.

To Find: The fundamental frequency

Solution:

• It is to be noted that for an organ pipe open at both ends we need to follow a simple trick. When both ends are open then the fundamental frequency is equal to the difference between the adjacent ( or nearest ) harmonics.
• If one end of the organ  pipe is open and the other is closed, in such cases, we need to use the formula;

                  f = nv / 4l     where l = length of pipe, v = velocity

Coming to the numerical,

It is said that both the ends are open, so we know that the fundamental frequency is equal to the difference between the adjacent harmonics which are 200 Hz and 240 Hz.

∴ Fundamental frequency = ( 240 - 200 ) Hz

                                             = 40 Hz

Hence, the fundamental frequency is 40 Hz.

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