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Chapter 17: Q3. (page 455)

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

Expert verified

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

01

Given Information

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

02

Part a)

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

03

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)

04

Part c)

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

05

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.

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Most popular questions from this chapter

In a laboratory experiment, one end of a horizontal string is tied

to a support while the other end passes over a frictionless pulley

and is tied to a 1.5 kg sphere. Students determine the frequencies

of standing waves on the horizontal segment of the string, then

they raise a beaker of water until the hanging 1.5 kg sphere is

completely submerged. The frequency of the fifth harmonic with

the sphere submerged exactly matches the frequency of the third

harmonic before the sphere was submerged. What is the diameter

of the sphere?

The lowest note on a grand piano has a frequency of 27.5 Hz. The entire string is 2.00 m long and has a mass of 400 g. The vibrating section of the string is 1.90 m long. What tension is needed to tune this string properly?

Two in-phase loudspeakers emit identical 1000 Hz sound waves along the x-axis. What distance should one speaker be placed behind the other for the sound to have an amplitude 1.5 times that of each speaker alone?

|| The three identical loudspeakers

in FIGURE P17.71 play a 170 Hz tone

in a room where the speed of sound

is 340 m/s. You are standing 4.0 m

in front of the middle speaker. At

this point, the amplitude of the wave

from each speaker is a.

a. What is the amplitude at this

point?

b. How far must speaker 2 be moved

to the left to produce a maximum

amplitude at the point where you

are standing?

c. When the amplitude is maximum,

by what factor is the sound intensity

greater than the sound intensity from a single speaker?

When mass M is tied to the bottom of a long, thin wire suspended

from the ceiling, the wire’s second-harmonic frequency is

200 Hz. Adding an additional 1.0 kg to the hanging mass increases

the second-harmonic frequency to 245 Hz. What is M?
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