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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 in air is 340 m s–1).



Answer -

Answer: First (Fundamental); No

Length of the pipe, = 20cm = 0.2 m

Source frequency = nth normalmode of frequency, νn = 430 Hz

Speed of sound, v = 340 m/s

In a closed pipe, the nth normalmode of frequency is given by the relation:

Hence, the first mode of vibration frequency is resonantlyexcited by the given source.

In a pipe open at both ends, the nth modeof vibration frequency is given by the relation:

Since the number of the mode of vibration (n)has to be an integer, the given source does not produce a resonant vibration inan open pipe.

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