Question

The amplitude of a standing sound wave in a long pipe closed at the left end is sketched below. The vertical axis is the maximum displacement of the air, and the horizontal axis is along the length of the pipe. What is the harmonic number for the mode of oscillation illustrated?

1) 1
2) 2
3) 3
4) 4

Answer 1

The mode of oscillation with three-fourths of its wavelength in the tube corresponds to the third harmonic.

Step-by-step explanation:

The harmonic number for the mode of oscillation illustrated, where the standing wave has three-fourths of its wavelength in the tube, is the third harmonic. This is because the fundamental frequency (first harmonic) has a wavelength four times the length of the tube, and each subsequent overtone (or harmonic) fits an additional half wavelength into the tube. In the depicted mode, there are two additional half wavelengths (three halves total), indicating the third harmonic.