Chapter 6 Waves and Sound (Section 2)

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Chapter 6Waves and Sound(Section 2)
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6.2 Aspects of Wave Propagation

• In this section, we consider what waves do as
  they travel.
• For waves traveling along a surface or throughout
  space in three dimensions, it is convenient to
  use two different ways to represent the wave.
• We will call these the wave-front model and the
  ray model.

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6.2 Aspects of Wave Propagation

• The figure shows how each is used to illustrate a
  wave pulse on water as it travels from the point
  where it was produced.
• The wave front is a circle that shows the
  location of the peak of the wave pulse.

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6.2 Aspects of Wave Propagation

• A ray is a straight arrow that shows the
  direction a given segment of the wave is
  traveling.

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6.2 Aspects of Wave Propagation

• A laser beam and sunlight passing through a small
  hole in a window shade both approximate
  individual rays of light that we can see if there
  is dust in the air.

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6.2 Aspects of Wave Propagation

• On the other hand, the rays of water ripples are
  not visible, but we do see the wave fronts.

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6.2 Aspects of Wave Propagation

• For a continuous water wave, the wave fronts are
  concentric circles around the point of origin
  (the source of the wave) that represent
  individual peaks of the wave.

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6.2 Aspects of Wave Propagation

• The largest circle shows the position of the
  first peak that was produced.
• Each successive wave front is smaller because it
  came later and has not traveled as far.
• The distance between adjacent wave fronts is
  equal to the wavelength of the wave.

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6.2 Aspects of Wave Propagation

• Again, a continuous wave is like a series of wave
  pulses produced one after another.
• The rays used to represent a continuous wave are
  lines radiating from the source of the wave (the
  blue arrows in the figure).

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6.2 Aspects of Wave Propagation

• The wave fronts arriving at a point far from the
  source are nearly straight lines (far right in
  the figure).
• The corresponding rays are nearly parallel.

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6.2 Aspects of Wave Propagation

• For a wave moving in three-dimensional space,
  like the sound traveling outward from you in all
  directions as you shout or whistle, the wave
  fronts are spherical shells surrounding the
  source of the wave.
• The wave front of a wave pulse, such as the sound
  from a hand clap, expands like a balloon that is
  being inflated very rapidly.

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6.2 Aspects of Wave Propagation

• For continuous three-dimensional waves such as a
  steady whistle, the wave fronts form a series of
  concentric spherical shells that expand like the
  circular wave fronts of a wave on a surface.
• A 440-hertz tuning fork produces 440 of these
  wave fronts each second.
• The surface of each wave front expands outward
  with a speed of 344 m/s (at room temperature).
• As with waves on a surface, the rays used to
  represent a continuous wave in three dimensions
  are lines radiating outward from the wave source.

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6.2 Aspects of Wave Propagation

• One inherent aspect of the propagation of waves
  on a surface or in three dimensions is that the
  amplitude of the wave necessarily decreases as
  the wave gets farther from the source.
• A certain amount of energy is expended to create
  a wave pulse or each cycle of a continuous wave.

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6.2 Aspects of Wave Propagation

• This energy is distributed over the wave front
  and determines the amplitude of the wave
• The greater the amount of energy given to a wave
  front, the larger the amplitude.
• As the wave front moves out, it gets larger, so
  this energy is spread out more and becomes less
  concentrated.
• This attenuation accounts for the decrease in
  loudness of sound as a noisy car moves away from
  you and for the decrease in brightness of a
  lightbulb as you move away from it.

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6.2 Aspects of Wave Propagation

• One can infer when the amplitude of a wave is
  changing by noting changes in the wave front or
  the rays. If the wave fronts are growing larger,
  then the amplitude is getting smaller.
• The same thing is indicated when the rays are
  diverging (slanting away from each other).

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6.2 Aspects of Wave Propagation

• At great distances from the source of a
  three-dimensional wave, the wave fronts become
  nearly flat and are called plane waves.
• The corresponding rays are parallel, and the
  waves amplitude stays constant.
• The light and other radiation we receive from the
  Sun come as plane waves because of the great
  distance between Earth and the Sun.
• With this background, we will look at several
  phenomena associated with wave propagation.

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6.2 Aspects of Wave PropagationReflection

• A wave is reflected whenever it reaches a
  boundary of its medium or encounters an abrupt
  change in the properties (density, temperature,
  and so on) of its medium.
• A wave pulse traveling on a rope is reflected
  when it reaches a fixed end.

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6.2 Aspects of Wave PropagationReflection

• It bounces off the end and travels back along
  the rope.
• Notice that the reflected pulse is inverted.
• When the end of the rope is attached to a very
  light (but strong) string instead, the reflected
  pulse is not inverted.

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6.2 Aspects of Wave PropagationReflection

• The incoming pulse causes two pulses to leave the
  junction, a reflected pulse and a pulse that
  continues into the light string.
• This reflection occurs because of an abrupt
  change in the density of the medium from high
  density (for the heavy rope) to low density (for
  the light string).

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6.2 Aspects of Wave PropagationReflection

• Similarly, a wave on a surface or a wave in three
  dimensions is reflected when it encounters a
  boundary.
• The wave that bounces back is called the
  reflected wave.
• Rays are more commonly used to illustrate
  reflection because they nicely show how the
  direction of each part of the wave is changed.

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6.2 Aspects of Wave PropagationReflection

• When a wave is reflected from a straight boundary
  (for surface waves) or a flat boundary (in three
  dimensions), the reflected wave appears to be
  expanding out from a point behind the boundary.

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6.2 Aspects of Wave PropagationReflection

• This point is called the image of the original
  wave source.
• An echo is a good example sound that encounters
  a large flat surface, such as the face of a
  cliff, is reflected and sounds like it is coming
  from a point behind the cliff.

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6.2 Aspects of Wave PropagationReflection

• Our most common experience with reflection is
  that of light from a mirror.
• The image that you see in a mirror is a
  collection of reflected light rays originating
  from the different points on the object you see.

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6.2 Aspects of Wave PropagationReflection

• Reflection from surfaces that are not flat (or
  straight) can cause interesting things to happen
  to waves.
• The figure shows a wave being reflected by a
  curved surface.
• Note that the rays representing the reflected
  part of the wave are converging toward each
  other.

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6.2 Aspects of Wave PropagationReflection

• This means that the amplitude of the wave is
  increasingthe wave is being focused.
• Parabolic microphones seen on the sidelines of
  televised football games use this principle to
  reinforce the sounds made on the playing field.
• Satellite receiving dishes do the same with radio
  waves.

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6.2 Aspects of Wave PropagationReflection

• A reflector in the shape of an ellipse has a
  useful property.
• Recall that the orbits of satellites, comets, and
  planets can be ellipses.
• An ellipse has two points in its interior called
  foci (the plural of focus).
• If a wave is produced at one focus, it will
  converge on the other focus after reflecting off
  the elliptical surface.
• All rays originating from one focus reflect off
  the ellipse and pass through the other focus.

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6.2 Aspects of Wave PropagationReflection

• A room shaped like an ellipse is called a
  whispering chamber because a person standing at
  one focus can hear faint soundseven
  whisperingproduced at the other focus.
• This property of the ellipse is also used in the
  medical treatment of kidney stones.

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6.2 Aspects of Wave PropagationDoppler Effect

• Can you recall the last time a fast-moving
  emergency vehicle with its siren blaring passed
  near you?
• If so, you may remember that the pitch or tone of
  its sound dropped suddenly as it went by
• Although, you may be so used to this phenomenon
  that you didnt notice it.

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6.2 Aspects of Wave PropagationDoppler Effect

• This is a manifestation of the Doppler effect
• The apparent change in the frequency of wave
  fronts emitted by a moving source, perhaps a
  tugboat floating down a river or a train
  traveling along a track, each blowing its horn.
• Each wave front expands outward from the point
  where the source was when it emitted that wave
  front.

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6.2 Aspects of Wave PropagationDoppler Effect

• In contrast to what is shown in the figure, where
  the source is stationary, ahead of the moving
  source, the wave fronts are bunched together.

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6.2 Aspects of Wave PropagationDoppler Effect

• This means that the wavelength is shorter than
  when the source is at rest, and therefore the
  frequency of the wave is higher.
• Behind the moving source, the wave fronts are
  spread apart
• The wavelength is longer, and the frequency is
  lower than when the source is motionless.

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6.2 Aspects of Wave PropagationDoppler Effect

• In both places, the higher the speed of the wave
  source, the greater the change in frequency.
• Note The speed of a wave in a medium is constant
  and is not affected by any motion associated with
  the wave source.
• Thus, if the wavelength goes up, the frequency
  must go down, and vice versa, to yield a constant
  wave speed v lf

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6.2 Aspects of Wave PropagationDoppler Effect

• The frequency of sound that reaches a person in
  front of a moving train is higher than that
  perceived when the train is not moving.
• A person behind the moving train hears a lower
  frequency.
• As a train or a fast car moves by, you hear the
  sound shift from a higher frequency (pitch) to a
  lower frequency.
• The change in the loudness of the sound, which
  you also hear, is not part of the Doppler effect
  
• it involves a separate process

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6.2 Aspects of Wave PropagationDoppler Effect

• A similar shift in frequency of sound occurs if
  you are moving toward a stationary sound source.

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6.2 Aspects of Wave PropagationDoppler Effect

• This Doppler shift happens because the speed of
  the wave relative to you is higher than that when
  you are not moving.
• The wave fronts approach you with a speed equal
  to the wave speed plus your speed.
• Because the wavelength is not affected, the
  equation v fl tells us that the frequency of
  the wave is increased in proportion to the speed
  of the wave relative to you.
• By the same reasoning, when one is moving away
  from the sound source, the frequency is reduced.

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6.2 Aspects of Wave PropagationDoppler Effect

• The Doppler effect occurs for both sound and
  light and is routinely taken into account by
  astronomers.
• The frequencies of light emitted by stars that
  are moving toward or away from Earth are shifted.
  
• If the speed of the star is known, the original
  frequencies of the light can be computed.
• If the frequencies are known instead, the speed
  of the star can be computed from the amount of
  the Doppler shift.
• Such information is essential for determining the
  motions of stars in our galaxy or of entire
  galaxies throughout the universe.

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6.2 Aspects of Wave PropagationDoppler Effect

• Echolocation is the process of using the waves
  reflected from an object to determine its
  location. Radar and sonar are two examples.
• Basic echolocation uses reflection only
• A wave is emitted from a point, reflected by an
  object of some kind, and detected on its return
  to the original point.
• The time between the emission of the wave and the
  detection of the reflected wave (the round-trip
  time) depends on the speed of the wave and the
  distance to the reflecting object.

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6.2 Aspects of Wave PropagationDoppler Effect

• For example, if you shout at a cliff and hear the
  echo 1 second later, you know that the cliff is
  approximately 172 meters away.
• This is because the sound travels a total of 344
  meters (172 meters each way) in 1 second (at room
  temperature).
• If it takes 2 seconds, the cliff is approximately
  344 meters away, and so on.

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6.2 Aspects of Wave PropagationDoppler Effect

• With sonar, a sound pulse is emitted from an
  underwater speaker, and any reflected sound is
  detected by an underwater microphone.
• The time between the transmission of the pulse
  and the reception of the reflected pulse is used
  to determine the distance to the reflecting
  object.
• Basic radar uses a similar process with
  microwaves that reflect off aircraft, raindrops,
  and other things.

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6.2 Aspects of Wave PropagationDoppler Effect

• Incorporating the Doppler effect in echolocation
  makes it possible to immediately determine the
  speed of an approaching or departing object.
• A moving object causes the reflected wave to be
  Doppler shifted.
• If the frequency of the reflected wave is higher
  than that of the original wave, the object is
  moving toward the source.
• If the frequency is lower, then the object is
  moving away.

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6.2 Aspects of Wave PropagationDoppler Effect

• Doppler radar uses this combination of
  echolocation and the Doppler effect.
• The time between transmission and reception gives
  the distance to the object, whereas the amount of
  frequency shift is used to determine the speed.
• Law-enforcement officers use Doppler radar to
  check the speeds of vehicles, and Doppler radar
  is also used in base-ball, tennis, and other
  sports to clock the speed of a ball.

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6.2 Aspects of Wave PropagationDoppler Effect

• Dust, raindrops, and other particles in air
  reflect microwaves, making it possible to detect
  the rapidly swirling air in a tornado with
  Doppler radar.
• Another potentially life-saving application is
  the detection of wind sheardrastic changes in
  wind speed near storms that have caused
  low-flying aircraft to crash.

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6.2 Aspects of Wave PropagationBow Waves and
Shock Waves

• In the previous discussion, we have implicitly
  assumed that the speed of the wave source is much
  less than the wave speed itself.
• However, if youve ever heard a sonic boom or
  been jostled by the wake of a passing watercraft
  while floating in the water, youve had
  experience with circumstances where the reverse
  is true.

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6.2 Aspects of Wave PropagationBow Waves and
Shock Waves

• The figure shows another series of wave fronts
  produced by a moving wave source.
• This time the speed of the wave source is greater
  than the wave speed.
• The wave fronts pile up in the forward
  direction and form a large-amplitude wave pulse
  called a shock wave.
• This is what causes the V-shaped bow waves
  produced by swimming duck and moving boats.

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6.2 Aspects of Wave PropagationBow Waves and
Shock Waves

• Aircraft flying faster than the speed of sound
  produce a similar shock wave.
• In this case, the three-dimensional wave fronts
  form a conical shock wave, with the aircraft at
  the cones apex.
• This conical wave front moves with the aircraft
  and is heard as a sonic boom (a sound pulse) by
  persons on the ground.

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6.2 Aspects of Wave PropagationDiffraction

• Think about walking down a street and passing by
  an open door or window with sound coming from
  inside.
• You can hear the sound even before you get to the
  opening, as well as after youve passed it.
• The sound doesnt just go straight out of the
  opening like a beam, it spreads out to the sides.
  
• This is diffraction.

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6.2 Aspects of Wave PropagationBow Waves and
Shock Waves

• The figure shows wave fronts as they reach a gap
  in a barrier.
• These might be sound waves passing through a door
  or ocean waves encountering a breakwater.
• The part of the wave that passes through the gap
  actually sends out wave fronts to the sides as
  well as ahead.
• The rays that represent this process show that
  the wave bends around the edges of the
  opening.

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6.2 Aspects of Wave PropagationBow Waves and
Shock Waves

• The extent to which the diffracted wave spreads
  out depends on the ratio of the size of the
  opening to the wavelength of the wave.
• When the opening is much larger than the
  wavelength, there is little diffraction
• The wave fronts remain straight and do not spread
  out to the sides appreciably.
• This is what happens when light comes in through
  a window.
• The wavelength of light is less than a millionth
  of a meter, and consequently, there is little
  diffraction.

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6.2 Aspects of Wave PropagationBow Waves and
Shock Waves

• When the wavelength is roughly the same size as
  the opening, the diffracted wave spreads out much
  more.

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6.2 Aspects of Wave PropagationBow Waves and
Shock Waves

• The sizes of windows and doors are well within
  the range of the wavelengths of sound waves, so
  sound diffracts a great deal after passing
  through them.
• Higher frequencies (shorter wavelengths) are not
  diffracted as much as the lower frequencies.

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6.2 Aspects of Wave PropagationInterference

• Interference arises when two continuous waves,
  usually with the same amplitude and frequency,
  arrive at the same place.
• The sound from a stereo with the same steady tone
  coming from each speaker is an example of this
  situation.
• Another way to cause interference is to direct a
  continuous wave at a barrier with two openings in
  it.
• The two waves that emerge from the two openings
  will diffract (spread out), overlap each other,
  and undergo interference.

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6.2 Aspects of Wave PropagationInterference

• Consider the case of identical, continuous water
  waves produced by two small objects made to
  oscillate up and down in unison on the surface of
  the water.
• As these two waves travel outward, each point in
  the surrounding water moves up and down under the
  influence of both waves.
• If we move around in an arc about the wave
  sources, we find that at some places the water is
  moving up and down with a large amplitude.
• At other places, the water is actually stillit
  is not oscillating at all.

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6.2 Aspects of Wave PropagationInterference
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6.2 Aspects of Wave PropagationInterference

• To see why this characteristic pattern of
  large-amplitude and zero-amplitude motion arises,
  consider the figure below, a sketch showing two
  waves at one moment in time.
• The thicker lines represent peaks of the waves,
  and the thinner lines represent the valleys.

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6.2 Aspects of Wave PropagationInterference

• In the figure shown, the straight lines labeled C
  indicate the places where the two waves are in
  phasethe peak of one wave matches the peak of
  the other, and valley matches valley.
• The two waves reinforce each other, and the
  amplitude is large.
• This is called constructive interference.

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6.2 Aspects of Wave PropagationInterference

• On the straight lines labeled D, the waves are
  out of phasethe peak of one wave matches the
  valley of the other.
• The two waves cancel each other.
• Whenever one wave has upward displacement, the
  other has downward displacement, and vice versa.
  Therefore, the net displacement is always zero.
• This is called destructive interference.

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6.2 Aspects of Wave PropagationInterference

• This figure shows the same waves a short time
  later after the waves have traveled one-half of a
  wavelength.
• The pattern of constructive and destructive
  interference is not altered as the waves travel
  outward.

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6.2 Aspects of Wave PropagationInterference

• If the photograph shown had been taken earlier or
  later, it would look the same.

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6.2 Aspects of Wave PropagationInterference

• Whether the two waves are in phase or out of
  phase depends on the relative distances they
  travel.
• To reach any point on line C1 in the figure, the
  two waves travel the same distance and
  consequently arrive with peak matching peak and
  valley matching valley.

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6.2 Aspects of Wave PropagationInterference

• Along the line C2, the wave from the source on
  the left must travel a distance equal to one
  wavelength farther than the wave from the source
  on the right.
• The reverse is true along the line on the left
  labeled C.
• In general, there is constructive interference at
  all points where one wave travels one, or two, or
  three . . . wavelengths farther than the other
  wave.

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6.2 Aspects of Wave PropagationInterference

• On the other hand, along the line of destructive
  interference labeled D1, the wave from the source
  on the left has to travel one-half wavelength
  farther than the wave from the source on the
  right.
• They arrive with peak matching valley and cancel
  each other.

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6.2 Aspects of Wave PropagationInterference

• Along the far-right line labeled D, the wave from
  the source on the left has to travel wavelengths
  farther, so the two waves again arrive out of
  phase.
• The reverse is true for the lines showing
  destructive interference on the left.

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6.2 Aspects of Wave PropagationInterference

• In general, there is destructive interference at
  all points where one wave travels ½ , or 1 ½ , or
  2 ½ , . . . wavelengths farther than the other
  wave.
• At places in between constructive and destructive
  interference, the waves are not completely in
  phase or out of phase, so they partially
  reinforce or cancel each other.

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6.2 Aspects of Wave PropagationInterference

• Sound and other longitudinal waves can undergo
  interference in the same way.
• We can imagine the figure representing sound
  waves with the peaks corresponding to
  compressions and the valleys corresponding to
  expansions.

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6.2 Aspects of Wave PropagationInterference

• Along the lines of constructive interference, one
  would hear a loud, steady sound.
• Along the lines of destructive interference, one
  would hear no sound at all.