Principles of Technology CH 12 Wave and Sound 3
Name________
KEY OBJECTIVES
At the conclusion of this chapter you will be able to:
• Define the terms constructive interference, destructive interference, resonance, and diffraction.
• Explain how interference can produce standing waves and beats.
• Define the term Doppler effect, and explain this phenomenon.
12.7 INTERFERENCE
Two or more waves passing simultaneously through the same area of a medium affect the medium
independently but do not affect each other. The resultant displacement of any point in the medium is the
algebraic sum of the displacements of all the individual waves; this is known as the principle of
superposition, and the result is called interference.
There exist two kinds of interference, constructive and destructive. Constructive interference occurs
when the individual wave displacements, A and B in the diagram below, are in the same direction. In this
case, the resulting amplitude, A+ B, is greater than any individual wave amplitude.
1.
Which statement is false?
a. Two or more waves passing simultaneously through the same area of a medium affect the medium
independently but do not affect each other.
b. The resultant displacement of any point in the medium is the algebraic sum of the displacements of all
the individual waves; this is known as the principle of superposition, and the result is called interference.
c. There exist only one kind of interference, constructive interference.
d. Constructive interference occurs when the individual wave displacements, A and B are in the same
direction and the resulting amplitude is greater than any individual wave amplitude.
Destructive interference occurs when displacements A and B are in opposite directions, as illustrated below.
In this case, the resulting amplitude is less than any individual wave amplitude. If the displacements are
equal in magnitude, complete or maximum destructive interference occurs. If the displacements are not
equal in magnitude, the result is partial destructive interference.
2.
Which statement is false?
a. Destructive interference occurs when displacements are in opposite directions.
b. In destructive interference, the resulting amplitude is less than any individual wave amplitude.
c. In destructive interference if the displacements are equal in magnitude, complete or maximum destructive
interference occurs and if the displacements are not equal in magnitude, the result is partial destructive
interference.
d. In destructive interference, the resulting amplitude is greater than any individual wave amplitude
12.8 STANDING WAVES
The diagram illustrates a wave being continuously produced by an up- and-down
motion on a string traveling toward a barrier and the reflected wave emerging from
it. The incident and reflected waves have the same frequencies and amplitudes, but
they are traveling in opposite directions. When the waves pass one another, they
will interfere regularly, both constructively and destructively.
This interference will produce a wave that appears to “stand still” in the horizontal
direction. Adjacent crests and troughs will move vertically in opposite directions
about points that have no motion; the result is known as a standing wave. The points
that do not move are called nodes, and the crest-trough combinations are antinodes.
The diagram below illustrates this phenomenon.
3.
Which statement is false?
a. When a wave being is continuously produced by an up- and-down motion on a string traveling toward a barrier
and the reflected wave emerging from it there will be no interference of the incident and reflected waves.
b. When the incident and reflected waves have the same frequencies and amplitudes, but are traveling in opposite
directions hey will interfere regularly, both constructively and destructively when the waves pass one another.
c. The incident and reflected waves interference will produce a wave that appears to “stand still” in the horizontal
direction with adjacent crests and troughs will move vertically in opposite directions about points that have no
motion; the result is known as a standing wave.
d. The points that do not move are called nodes and the crest-trough combinations are antinodes.
12.9 RESONANCE
If a person were to pluck a stretched guitar string that was not connected to a guitar, the sound would not be
heard. What exactly does the guitar body contribute to the production of audible sounds?
When a string is plucked, a standing wave pattern is established in the string. The guitar box is capable of
vibrating at the frequencies produced by the strings, and a standing-wave pattern is established in the guitar
itself. This phenomenon is known as resonance. The amplitudes of the standing waves in the guitar are
much larger than those in the string, however, and therefore we hear the sound. In general, musical
instruments act as resonance devices.
Sometimes, resonance can be an unwanted phenomenon. Years ago, a gale-force wind caused a bridge in
Tacoma, Washington, to resonate at its natural frequency of vibration. The energy produced by the standingwave pattern was great enough to cause the bridge to collapse. When bridges and like structures are built
today, devices are incorporated to prevent the production of these destructive standing-wave patterns.
4.
Which statement is false?
a. When a guitar string is plucked, a standing wave pattern is established in the string. The guitar box is capable of
vibrating at the frequencies produced by the strings, and a standing-wave pattern is established in the guitar
itself. This phenomenon is known as resonance.
b. The amplitudes of the standing waves in the guitar are much larger than those in the string, however, and
therefore we hear the sound. In general, musical instruments act as resonance devices.
c. Plucking a lone guitar string is louder than plucking the same string connected to a guitar.
d. The energy produced by the resonance of machines and structures at their natural frequency may be great
enough to cause a collapse or breakdown. When bridges and like structures are built today, devices are
incorporated to prevent the production of these destructive standing-wave patterns.
12.10 BEATS
If two waves of the same frequency and amplitude interfere
constructively, they will produce a single wave with the same frequency
and twice the amplitude. If the waves interfere destructively, they will
cancel each other. Suppose two sound waves with nearly the same frequencies (e.g., 256 Hz and 258 Hz)
interact with one another. What will happen then?
The result of this interaction will be the production of a “warbling” sound,
that is, a sound that is alternately louder and softer. In this case, the
alternation will occur 2 times per second, and the frequency of this sound
will be 257 Hz.
This phenomenon, known as beats is illustrated, is the result of a regularly alternating pattern of constructive
and destructive interference. The number of beats per second (the beat frequency) is found by subtracting
the smaller frequency from the larger one; the frequency of the resulting wave (i.e., the pitch of the sound
wave) is the average of the two frequencies.
5.
Which statement is false?
a. If two waves of the same frequency and amplitude interfere constructively, they will produce a single wave with
the same frequency and twice the amplitude. If two waves of the same frequency and amplitude interfere
destructively, they will cancel each other.
b. If two sound waves with very small frequencies interact with one another, the result of this interaction will be
single wave with the very large amplitude.
c. If two sound waves with nearly the same frequencies (e.g., 256 Hz and 258 Hz) interact with one another, the
result of this interaction will be the production of a “warbling” sound, that is, a sound that is alternately louder
and softer. In this case, the alternation will occur 2 times per second, and the frequency of this sound will be
257 Hz.
d. The phenomenon, known as beats, is the result of a regularly alternating pattern of constructive and destructive
interference. The number of beats per second (the beat frequency) is found by subtracting the smaller frequency
from the larger one; the frequency of the resulting wave (i.e., the pitch of the sound wave) is the average of the
two frequencies.
PROBLEM
A person hears tones of 440 hertz and 444 hertz simultaneously. Calculate
(a) the number of beats heard each second and
(b) the pitch of the resultant sound.
SOLUTION
(a) The number of beats per second (the beat frequency) is found by subtracting the smaller frequency
from the larger one:
444 Hz — 440 Hz = 4 beats/s
(b) The pitch of the resulting wave is the average of the two frequencies:
(444 Hz + 440 Hz) / 2 = 442Hz
6.
Calculate the number of beats heard each second when a person hears tones of 320 hertz and 328
hertz simultaneously.
a. 2 beats/s
b. 4 beats/s
c. 6 beats/s
d. 8 beats/s
7.
Calculate the pitch of the resultant sound when a person hears tones of 320 hertz and 328 hertz
simultaneously.
a. 8 Hz
b. 40 Hz
c. 324 Hz
d. 450 Hz
8.
Calculate the number of beats heard each second when a person hears tones of 208
220 hertz simultaneously.
a. 6 beats/s
b. 12 beats/s
c. 210 beats/s
d. 430 beats/s
hertz and
9.
Calculate the pitch of the resultant sound when a person hears tones of 208 hertz and 220 hertz
simultaneously.
a. 180 Hz
b. 214 Hz
c. 324 Hz
d. 428 Hz
10. Calculate the beat frequency heard each second when a person hears tones of 124
142 hertz simultaneously.
a. 18 beats/s
b. 120 beats/s
c. 140 beats/s
d. 270 beats/s
hertz and
11. Calculate the pitch of the resultant sound when a person hears tones of 124 hertz and 142 hertz
simultaneously.
a. 133 Hz
b. 180 Hz
c. 266 Hz
d. 1760 Hz
12.11 DIFFRACTION
Diffraction is the bending of a wave around an obstacle. If a person stands beside an open door, he or she
can usually hear conversation taking place in the room. As the sound waves emerge through the door, they
are able to “bend around” the doorway. Similarly, water waves seem to be able to pass through pier barriers
as though no obstruction were present.
The requirement for diffraction is that the size of the opening be on the order of the length of the wave being
diffracted. For this reason, light will not diffract through a doorway because the opening is far too large in
comparison to the wavelength of light. We will examine how wave diffraction occurs in Chapter 13.
12.
Which statement is false?
a. Water waves are able to pass through pier barriers as though no obstruction were present due to diffraction.
b. Diffraction is the bending of a wave around an obstacle. The requirement for diffraction is that the size of the
opening be on the order of the length of the wave being diffracted.
c. Sound will not diffract through a doorway because the opening is far too large in comparison to the wavelength
of sound so if a person stands beside an open door, he or she would never be able to hear a conversation taking
place in the room.
d. Light will not diffract through a doorway because the opening is far too large in comparison to the wavelength
of light.
12.12 DOPPLER EFFECT
All of us are familiar with the sound of a siren on a moving vehicle—a fire engine, for example. As the
vehicle approaches, the apparent pitch of the siren is increased; as the vehicle passes us and then recedes,
the apparent pitch is decreased.
This phenomenon, known as the Doppler Effect, occurs with all types of waves, including light. It is the
result of relative motion between a source of waves and an observer. As the distance between the source and
the observer decreases, the frequency of the source, as perceived by the observer, is increased; as the
distance increases, the apparent frequency is decreased.
13.
Which statement is false?
a. As a train approaches, the apparent pitch of the horn is increased; as the train passes us and then recedes, the
apparent pitch is decreased.
b. The phenomenon, known as the Doppler Effect, occurs with all types of waves, including light. It is the result of
relative motion between a source of waves and an observer.
c. As the distance between the source and the observer decreases, the frequency of the source, as perceived by the
observer, is increased. As the distance between the source and the observer increases, the apparent frequency is
decreased.
d. The Doppler Effect can not be seen or heard and thus is rarely observed and only at great cost.
Effect on Mechanical and Electromagnetic Waves
For mechanical waves, such as sound and water, the effect produced by a source
in motion is different from the effect experienced by an observer in motion, even
though the general outcome for both is similar. For example, if an observer is
moving toward a stationary source of sound, his or her ear drum receives more
waves than if the observer were at rest, and the apparent frequency of the sound is
increased. If, however, the source is moving toward a stationary observer, the
result is a series of sound waves that are crowded together on the side nearest the
observer. The result is that the observer’s ear drum receives more waves than if
the source were at rest, and the frequency of the sound appears to be increased.
The following diagram illustrates the situation in which a source of sound is in
motion and the observers are stationary.
For electromagnetic waves, such as visible light, the frequency change is recorded as a color shift, a
phenomenon important in astronomy and astrophysics.
14.
Which statement is false?
a. For mechanical waves, such as sound and water, the effect produced by a source in motion is different from the
effect experienced by an observer in motion, even though the general outcome for both is similar.
b. For sound waves, the amplitude change caused by the Doppler Effect is recorded as a beat shift, a phenomenon
important in music.
c. If an observer is moving toward a stationary source of sound, his or her ear drum receives more waves than if
the observer were at rest, and the apparent frequency of the sound is increased. If the source is moving toward a
stationary observer, the result is a series of sound waves that are crowded together on the side nearest the
observer. The result is that the observer’s ear drum receives more waves than if the source were at rest, and the
frequency of the sound appears to be increased.
d. For electromagnetic waves, such as visible light, the frequency change is recorded as a color shift, a
phenomenon important in astronomy and astrophysics.
Bow Waves, Shock Waves, and Sonic Booms
If you have ever seen a duck swimming on a lake or pond, you may have observed a V-shaped wave
produced by the duck. This phenomenon, known as a bow wave, is also produced by a boat in motion on a
body of water. A bow wave is a special case of the Doppler effect. As the duck (or boat) travels on the
water, it produces water waves. If the speed of the traveler is greater than the speed of the water waves, a
bow wave results.
When planes exceed the speed of sound, they produce shock waves, which are exactly analogous to bow
waves. The diagram below illustrates how shock waves are formed. A shock wave is accompanied by an
explosion like sound known as a sonic boom.
15.
Which statement is false?
a. If you have ever seen a duck swimming on a lake or pond, you may have observed a V-shaped wave produced by
the duck, this is a bow wave which is the result of the Doppler effect and is a special case of the Doppler effect.
b. The phenomenon known as a bow wave is produced when a stone is dropped in a body of water.
c. As a duck (or boat) travels on the water, it produces water waves. If the speed of the traveler is greater than the
speed of the water waves, a bow wave results.
d. When planes exceed the speed of sound, they produce shock waves, which are exactly analogous to bow waves. A
shock wave is accompanied by an explosion like sound known as a sonic boom.
Summary
The characteristics of a periodic wave include speed, wavelength, frequency and period, and amplitude. Among the
properties of periodic waves are reflection, refraction (the change in the direction of a wave that enters a medium at
an angle), interference (the combination of two or more waves simultaneously in a medium), diffraction (the
apparent “bending” of a wave around an obstacle), and the Doppler effect (the apparent change in the frequency of
a wave as perceived by an observer because of the relative motion between the wave source and the observer).