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?

a) Second harmonic
b) Third harmonic
c) Fourth harmonic
d) Fifth harmonic
e) Sixth harmonic

Answer 1

The harmonic number for the mode of oscillation illustrated, where the pipe shows three-fourths of a wavelength for a standing wave in a long pipe closed at one end, is the third harmonic (first overtone).

Step-by-step explanation:

The mode of oscillation illustrated by the standing wave in a long pipe closed at one end implies that the tube resonates at a frequency higher than the fundamental frequency. Since the illustration is not provided, we infer from the textual description that the standing wave shown has three-fourths of a wavelength (¾λ) inside the tube. For a pipe that is closed at one end, the resonant frequencies form an odd harmonic series: first harmonic (fundamental), third harmonic (first overtone), fifth harmonic (second overtone), and so on. If the pipe shows three-fourths of a wavelength, this correlates to the first overtone, which is the third harmonic. Therefore, the harmonic number for the mode of oscillation illustrated would be the third harmonic.