Question

FIGURE Q17.3 shows the displacement of a standing sound wave in a 32-cm-long horizontal tube of air open at both ends. a. What mode (m-value) is this? b. Are the air molecules moving horizontally or vertically? Explain. c. At what distances from the left end of the tube do the molecules oscillate with maximum amplitude? d. At what distances from the left end of the tube does the air pressure oscillate with maximum amplitude?

Short answer

a) This is 2nd Harmonic wave, (m = 2)

b) Air molecules are moving vertically

c) x = 0, 16 and 32

d) x = 8 and 24

Step-by-step solution

Given Information

A snapshot of a standing sound wave over the distance of 32cm.

Part a)

This is a 2nd Harmonic wave (m value = 2).

Part b)

Particles of the wave move vertically as in transverse waves particles move in the direction perpendicular to the direction of wave. (Sound waves are transverse waves)

Part c)

At distances 0cm, 16cm, and 32cm, molecules will oscillate at maximum amplitude.

Part d)

Air pressure is maximum at nodes of the sound wave, therefore air pressure will oscillate with maximum amplitude at x = 8cm and x = 24cm.