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Chapter 17: Q. 21 (page 483)

A longitudinal standing wave can be created in a long, thin aluminum rod by stroking the rod with very dry fingers. This is often done as a physics demonstration, creating a high-pitched, very annoying whine. From a wave perspective, the standing wave is equivalent to a sound standing wave in an open-open tube. As FIGURE EX17.21 shows, both ends of the rod are antinodes. What is the fundamental frequency of a 2.0-m-long aluminum rod?

Short Answer

Expert verified

The fundamental frequency of a 2.0-m-long aluminum rod is,1605Hz.

Step by step solution

01

Given data

Length of the aluminum rod is, L=2m

Both ends of the rod are antinodes. So, the rod is vibrating in the fundamental mode.

Consider speed of sound in aluminum is,v=6420m/s

02

Determination of frequency

For fundamental mode, the wavelength of sound wave can ne written as, λ1=2L

Therefore, the frequency of the longitudinal standing wave is,

f=vλ1⇒f=6420m/s2L⇒f=6420m/s2×2m⇒f=1605Hz

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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?

Piano tuners tune pianos by listening to the beats between the

harmonics of two different strings. When properly tuned, the note

A should have a frequency of 440 Hz and the note E should be

at 659 Hz.

a. What is the frequency difference between the third harmonic

of the A and the second harmonic of the E?

b. A tuner first tunes the A string very precisely by matching it to

a 440 Hz tuning fork. She then strikes the A and E strings simultaneously

and listens for beats between the harmonics. What

beat frequency indicates that the E string is properly tuned?

c. The tuner starts with the tension in the E string a little low,

then tightens it. What is the frequency of the E string when

she hears four beats per second?

Two loudspeakers in a 20oCroom emit 686 Hz sound waves

along the x-axis.

a. If the speakers are in phase, what is the smallest distance between the speakers for which the interference of the sound

waves is maximum destructive?

b. If the speakers are out of phase, what is the smallest distance

between the speakers for which the interference of the sound

waves is maximum constructive?

M?

FIGURE EX17.1 is a snapshot graph at t = 0 s of two waves approaching each other at 1.0 m/s. Draw six snapshot graphs, stacked vertically, showing the string at 1 s intervals from t = 1 s to t = 6 s

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