A 0.25-m string, vibrating in its sixth harmonic, excites a 0.96-m pipe that is open at both ends into its second overtone resonance. The speed of sound in air is 345 m/s. The common resonant frequency of the string and the pipe is closest to
A) 540 Hz.
B) 360 Hz.
C) 450 Hz.
D) 630 Hz.
E) 700 Hz.

Question

Quizplus · Accepted Answer

The sixth harmonic of the string is 6f, where f is the fundamental frequency. The second overtone of the pipe is 3f, where f is the fundamental frequency of the pipe. Since the string and the pipe are resonating at the same frequency, we have 6f = 3f, which gives f = 345 Hz. The common resonant frequency is then 6f = 6 * 345 Hz = 2070 Hz. The closest choice to this value is 540 Hz, which is the sixth harmonic of 90 Hz.

A 025-M String, Vibrating in Its Sixth Harmonic, Excites a 0