Question
A pipe 20 cm long is closed at one end. Which harmonic mode of the pipe is resonantly excited by a 430 Hz source? Will the same source be in resonance with the pipe if both ends are open? (speed of sound = 340 m/s)
Solution
Length of one end closed pipe is, L = 20 cm = 0.20m
Frequency of source is, v = 430 Hz
We know that the frequency of nth mode is given by,
Let nth mode of pipe be in resonance with the source.
Therefore,
Therefore, the fundamental mode of pipe is in resonance with the source.
If both the ends of pipe are open then frequency of nth mode is,
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Substituting the values, we get
n = 0.5, which is not possible. Therefore, if both the ends are open, then pipe cannot be in resonance with the source.
