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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 source of 1237.5 Hz? (sound velocity in air = 330 ms–1)
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Solution
Length of pipe
(Closed pipe)
l = 20 cm = 20 × 10–2m
`v_"funda" = v/(4L) = 330/(4 xx 20 xx 10^-2)` ......(For closed pipe)
`v_"funda" = (330 xx 100)/80` = 412.5 Hz
`v_"given"/v_"funda" = 1237.5/412.5` = 3
Hence, 3rd harmonic mode of the pipe is resonantly excited by the source of given frequency.
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