Q.
How are the stationary waves formed in a closed pipe ? Explain the various modes of vibrations in a closed pipe and establish the relation between their frequencies.
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Detailed Solution
An organ pipe is a cylindrical tube having an air column. If one end is closed and the other is open, it is known as a closed organ pipe.
At closed end always a node and at open end an antinode will generate.
Harmonics in Closed Pipes :
i) The first harmonic in a closed pipe should have a node at the closed end and an antinode at the open end, then the length of the pipe
The fundamental frequency
.......(1)
ii) The next possible harmonic with two nodes and two antinodes it is the third harmonic, then the length of the pipe
The frequency of the third harmonic (or) first overtone is given by
[from equation (1)]
iii) Similarly the next overtone in the closed pipe is only the fifth harmonic. It will have three antinodes and three nodes. Then the length of the pipe
Frequency of fifth harmonic (or) second overtone
from equation(1),(2)(3) the ratio of fundamental and next harmonics are 1 : 3 : 5 : ....

