How standing waves are formed in closed organ pipe? Also discuss normal modes of vibration of these pipes?
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Consider the different modes of vibration of an air column within a pipe closed at one end. Let L be the length of the pipe.
Stationary waves are formed within the air column when the time taken by the sound waves to produce a compression and rarefaction becomes equal to the time taken by the wave to travel twice the length of the tube. The standing waves are formed only for certain discrete frequencies.

In the first mode of vibration of the air column, there is one node and one antinode as shown in the figure above.
If l is the length of the wave in the fundamental mode of vibration,

In the second mode of vibration of the air column, two nodes and two antinodes are formed.

Thus, we see that the frequencies of the modes of vibrations are in the ratio n:n1:n2 = 1:3:5.
This shows that only odd harmonics are present in the modes of vibrations of the air column closed at one end.
Stationary waves are formed within the air column when the time taken by the sound waves to produce a compression and rarefaction becomes equal to the time taken by the wave to travel twice the length of the tube. The standing waves are formed only for certain discrete frequencies.

In the first mode of vibration of the air column, there is one node and one antinode as shown in the figure above.
If l is the length of the wave in the fundamental mode of vibration,

In the second mode of vibration of the air column, two nodes and two antinodes are formed.

Thus, we see that the frequencies of the modes of vibrations are in the ratio n:n1:n2 = 1:3:5.
This shows that only odd harmonics are present in the modes of vibrations of the air column closed at one end.
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In the first mode of vibration in the closed organ pipe, an antinode is formed at the open end and a node is formed at the close end.
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