The fundamental frequency of a pipe closed at one end is f. What is the frequency of the third harmonic?

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BlackTom AI · Accepted Answer

We start by recalling the harmonic series for a pipe closed at one end. Such a pipe supports only odd harmonics, with frequencies that are integer multiples of the fundamental f, but only for odd integers: f, 3f, 5f, ... .

Option 7f: This would correspond to the seventh harmonic, which is not part of the odd-harmonic sequence for a closed pipe and is far higher than the third harmonic. Therefore this is incorrect.

Option 3f: This matches the third harmonic (n = 3) of a pipe closed at one end. Since only odd harmonics occur, the sequence goes f, 3f, 5f, ... and 3f is precisely the frequency of the third mode. This option aligns with the established pattern for closed-end pipes, so it is consistent with the theory.

Option 5f: This is the fifth harmonic, which is the next odd multiple after 3f. While 5f is a valid harmonic for a closed pipe, it does not correspond to the third harmonic as asked in the question, making this option incorrect for the stated question.

Option 6f: This value represents an even multiple and is not allowed in the harmonic series of a pipe closed at one end. Since even harmonics do not exist in this configuration, this option is incorrect.

SPHY001 Practice Quiz - Unit 18 | LA058

The fundamental frequency of a pipe closed at one end is f. What is the frequency of the third harmonic?

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