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Chapter 17: Q. 37 (page 484)
A string vibrates at its third-harmonic frequency. The amplitude at a point 30 cm from one end is half the maximum amplitude. How long is the string?
The length of the string is 5.40 m
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A flutist assembles her flute in a room where the speed of
sound is 342 m/s. When she plays the note A, it is in perfect tune
with a 440 Hz tuning fork. After a few minutes, the air inside her
flute has warmed to where the speed of sound is 346 m/s.
a. How many beats per second will she hear if she now plays the
note A as the tuning fork is sounded?
|| 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?
||| A water wave is called a deep-water wave if the water’s depth
is more than one-quarter of the wavelength. Unlike the waves
we’ve considered in this chapter, the speed of a deep-water wave
depends on its wavelength:
v = B
gl
2p
Longer wavelengths travel faster. Let’s apply this to standing waves.
Consider a diving pool that is 5.0 m deep and 10.0 m wide. Standing
water waves can set up across the width of the pool. Because
water sloshes up and down at the sides of the pool, the boundary
conditions require antinodes at x = 0 and x = L. Thus a standing
water wave resembles a standing sound wave in an open-open tube.
a. What are the wavelengths of the first three standing-wave
modes for water in the pool? Do they satisfy the condition for
being deep-water waves?
b. What are the wave speeds for each of these waves?
c. Derive a general expression for the frequencies fm of the possible
standing waves. Your expression should be in terms of m, g, and L.
d. What are the oscillation periods of the first three standing wave
If you pour liquid into a tall, narrow glass, you may hear sound with a steadily rising pitch. What is the source of the sound? And why does the pitch rise as the glass fills?
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