The fundamental frequency of a pipe opened at both ends is f. What is the frequency of the third harmonic?

Question

BlackTom AI · Accepted Answer

This question asks about the harmonic series of a pipe that is open at both ends and the frequency of the third harmonic.
Option 1: 3f. In an open-open pipe, all harmonics are present and the nth harmonic frequency is n times the fundamental frequency f1. The third harmonic corresponds to n = 3, giving 3f. This aligns with the standard harmonic pattern for open pipes.
Option 2: 7f. This would imply a seventh harmonic, which is not the third harmonic. Since open-open pipes support all harmonics in order, 7f would be inconsistent with the asked third harmonic.
Option 3: 6f. While 6f would be a valid harmonic frequency (the sixth harmonic), it does not match the third harmonic, which is the third multiple of the fundamental.
Option 4: 9f. Similarly, 9f represents the ninth harmonic, not the third. For an open-open pipe, the third harmonic remains 3f, not 9f.
In summary, the fundamental relationship for an open-open pipe is F_n = n × f, where f is the fundamental frequency and n is 1, 2, 3, …; therefore, the third harmonic is 3f rather than any of the other multiples listed.

The fundamental frequency of a pipe opened at both ends is f. What is the frequency of the third harmonic? 单项选择题

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