Chapter 6 Waves and Sound (Section 1)

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Chapter 6Waves and Sound(Section 1)
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Sound Medicine

• The diagnosis kidney stones, a disease that
  sometimes afflicts people in their 20s and 30s.
• The condition is very painful, and can kill.
• Your options?
• One is surgery, but the operation itself is
  dangerous, and then there is a long and
  uncomfortable recuperation.
• But since the early 1980s, there has been an
  alternative that works in most cases
• You can have the stones pulverized with sound.
• No scalpels involved

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Sound Medicine

• The process is called extracorporeal shock-wave
  lithotripsy (ESWL).
• A device called a lithotripter focuses intense
  sound waves on the stones, which are broken into
  tiny fragments that can then pass out of the
  patients system.
• The sound is produced and focused outside of the
  bodyhence the term extracorporeal.

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Sound Medicine

• Some ESWL systems make use of a reflector based
  on the shape of an ellipse.
• An intense sound pulse (shock wave) produced at
  one focus bounces off the reflector and converges
  on the other focus.
• The reflector is positioned so that the stone is
  at that second focus.

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Sound Medicine

• Other lithotripters focus the sound with an
  acoustic lens in much the way a magnifying
  glass can be used to focus sunlight to start a
  fire.
• In both systems, the sound is produced and
  focused inside a water-filled cushion in
  similar to a balloon, that is pressed against the
  patients body.
• The sound never travels in air.

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Sound Medicine

• Why does the ESWL sound wave continue on target
  after it passes from water into a patient?
• What is it about sound waves that makes them
  useful for this and many other medical
  applications?
• Answers to such questions are found in the study
  of waves.

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Sound Medicine

• Waves in general and sound waves in particular
  are the main topics of this chapter.
• Waves are an integral part of our everyday lives.
  
• Whether playing a guitar, listening to a radio,
  clocking the speed of a thrown baseball, or
  having a kidney stone shattered, we are using a
  wave of some kind.

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Sound Medicine

• The two most often used sensessight and
  hearingare highly developed wave-detection
  mechanisms.
• In the first part of this chapter, we look at
  simple waves and examine some of their general
  properties.
• The remainder of the chapter is about soundhow
  it is produced, how it travels in matter, and how
  it is perceived by humans.

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6.1 WavesTypes and Properties

• Ripples moving over the surface of a still pond,
  sound from a radio speaker traveling through the
  air, a pulse bouncing back and forth on a piano
  string, light from the Sun illuminating and
  warming Earththese are all waves.

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6.1 WavesTypes and Properties

• We can feel the effects of some waves, such as
  earthquake tremors (called seismic waves), as
  they pass.
• Others, such as sound and light, we sense
  directly with our ears and eyes.
• Technology has given us numerous devices that
  produce or detect waves that we cannot sense
• microwaves, ultrasound, x-rays

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6.1 WavesTypes and Properties

• What are waves?
• Though many and diverse, they share some basic
  features.
• They all involve vibration or oscillation of some
  kind.
• Floating leaves show the vibration of the waters
  surface as ripples move by.
• Our ears respond to the oscillation of air
  molecules and give us the perception of sound.
• Also, waves move and carry energy yet do not have
  mass.
• The sound from a loudspeaker can break a
  wineglass even though no matter moves from the
  speaker to the glass.

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6.1 WavesTypes and Properties

• We can define a wave as follows
• Wave A traveling disturbance consisting of
  coordinated vibrations that transmit energy with
  no net movement of matter
• Sound, water ripples, and similar waves consist
  of vibrations of matterair molecules or the
  waters surface, for example.
• The substance through which such waves travel is
  called the medium of the wave.
• Particles of the medium vibrate in a coordinated
  fashion to form the wave.

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6.1 WavesTypes and Properties

• A rope stretched between two people is a handy
  medium for demonstrating a simple wave.

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6.1 WavesTypes and Properties

• A flick of the wrist sends a wave pulse down the
  rope.
• Each short segment of the rope is pulled upward
  in turn by its neighboring segment.
• The forces between the parts of the medium are
  responsible for passing along the wave.
• This kind of wave is not unlike a row of dominoes
  knocking each other over, except that the medium
  of a wave does not have to be reset after a
  wave goes by.

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6.1 WavesTypes and Properties

• Many wavessound, water ripples, waves on a
  roperequire a material medium.
• They cannot exist in a vacuum.
• On the other hand, light, radio waves,
  microwaves, and x-rays can travel through a
  vacuum because they do not require a medium for
  their propagation.
• We will take a close look at these special
  wavescalled electromagnetic wavesin chapter 8.

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6.1 WavesTypes and Properties

• Waves occur in a great variety of substances
• in gases (sound), liquids (water ripples), and
  solids (seismic waves through rock).
• Some travel along a line (a wave on a rope), some
  across a surface (water ripples), and some
  throughout space in three dimensions (sound).
• Many more examples could be listed.
• Clearly, waves are everywhere, and they are
  diverse in nature.

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6.1 WavesTypes and Properties

• A wave can be short and fleeting, called a wave
  pulse, or steady and repeating, called a
  continuous wave.
• The sound of a bursting balloon, a tsunami (large
  ocean wave generated by an earthquake), and the
  light from a camera flash are examples of wave
  pulses.
• The sound from a tuning fork and the light from
  the Sun are continuous waves.

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6.1 WavesTypes and Properties

• The figure shows a wave pulse and a continuous
  wave on a long rope.
• You can see that a continuous wave is like a
  series or train of wave pulses, one after
  another.

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6.1 WavesTypes and Properties

• If we take a close look at many different types
  of waves, we find that they can be classified
  according to the orientation of the wave
  oscillations.
• There are two main wave types transverse and
  longitudinal.

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6.1 WavesTypes and Properties

• Transverse Wave A wave in which the
  oscillations are perpendicular (transverse) to
  the direction the wave travels.
• Examples waves on a rope, electromagnetic waves,
  some seismic waves
• Longitudinal Wave A wave in which the
  oscillations are along the direction the wave
  travels.
• Examples sound in the air, some seismic waves

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6.1 WavesTypes and Properties

• Both types of waves can be produced on a Slinkya
  short, fat spring that you may have seen walk
  down steps.
• If a Slinky is stretched out on a flat, smooth
  tabletop, a transverse wave is produced by moving
  one end from side to side, perpendicular to the
  Slinkys length.

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6.1 WavesTypes and Properties

• A longitudinal wave is produced by pushing and
  pulling one end back and forth, first toward the
  other end, then back.
• For each type of wave, one can produce either a
  wave pulse or a continuous wave.

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6.1 WavesTypes and Properties

• A Slinky is not the only medium that can carry
  both transverse and longitudinal waves.
• Both kinds of waves can travel in any solid.
• Earthquakes and underground explosions produce
  both longitudinal and transverse seismic waves
  that travel through Earth.
• Simple waves that involve oscillation of atoms
  and molecules must be longitudinal to travel in
  liquids and gases because of the absence of rigid
  bonds between the particles.

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6.1 WavesTypes and Properties

• Many waves are neither purely longitudinal nor
  purely transverse.
• Although a water ripple appears to be a simple
  transverse wave, individual parcels of water
  actually move in circles or ellipsesthey
  oscillate forward and backward as well as up and
  down.
• Waves in plasmas and in the atmosphere are even
  more complicated.
• But the two simple types of waves described here
  are common and well suited for illustrating wave
  phenomena.

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6.1 WavesTypes and Properties

• The speed of a wave is the rate of movement of
  the disturbance.
• Do not confuse this with the speed of individual
  particles as they oscillate.
• For a given type of wave, the speed is determined
  by the properties of the medium.
• In the waves that we have been discussing, the
  masses of the particles that oscillate and the
  forces that act between them affect the wave
  speed.

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6.1 WavesTypes and Properties

• As a longitudinal wave, for example, travels on a
  Slinky, each coil is accelerated back and forth
  by its neighbors.
• Basic mechanics tells us that the mass of each
  coil and the size of the force acting on it will
  determine how quickly itand therefore the
  wavemoves.
• In general, weak forces or massive particles in a
  medium cause the wave speed to be low.

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6.1 WavesTypes and Properties

• Often, the speed of waves in a medium can be
  predicted by measuring some other properties of
  the medium.
• After all, the factors that affect wave
  speedparticles, masses, and interparticle
  forcesalso affect other properties of a
  substance.

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6.1 WavesTypes and Properties

• For example, the speed of waves on a stretched
  rope or a Slinky or on a taut wire can be
  computed by using the force F that must be
  exerted to keep it stretched and its linear mass
  density r, which equals its mass m divided by its
  length l.
• The symbol r represents the Greek letter rho,
  pronounced like row.

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6.1 WavesTypes and Properties

• In particular,
• Increasing this force, also called the tension,
  will cause the waves to move faster.
• This is how stringed instruments such as guitars
  and pianos are tuned.

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6.1 WavesTypes and PropertiesExample 6.1

• A student stretches a Slinky out on the floor to
  a length of 2 meters. The force needed to keep
  the Slinky stretched is measured and found to be
  1.2 newtons. The Slinkys mass is 0.3 kilograms.
• What is the speed of any wave sent down the
  Slinky by the student?

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6.1 WavesTypes and PropertiesExample 6.1

• First, we compute the Slinkys linear mass
  density
• The speed of waves on the Slinky is then

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6.1 WavesTypes and Properties

• The speed of sound in air or any other gas
  depends on the ratio of the pressure of the gas
  to the density of the gas.
• But for each gas, this ratio depends only on the
  temperature.
• In particular, the speed of sound in a gas is
  proportional to the square root of the Kelvin
  temperature

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6.1 WavesTypes and Properties

• For air,
• Although the air is thinner at higher altitudes,
  the speed of sound there is actually lower
  because the air is colder at these elevations.

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6.1 WavesTypes and PropertiesExample 6.2

• What is the speed of sound in air at room
  temperature (20?C 68?F)?
• The temperature in kelvins is
• Therefore,

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6.1 WavesTypes and Properties

• The numerical factor (20.1) in the equation in
  Example 6.2 is determined by the properties of
  the molecules that comprise air and therefore
  applies to air only.
• The speed of sound in any other gas will be
  different, and the corresponding equation for v
  will have a different numerical factor.
• Two examples

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6.1 WavesTypes and Properties

• For the remainder of this section, we will take a
  look at some of the properties of a continuous
  wave.
• A convenient example is a transverse wave on a
  Slinky produced by moving one end smoothly side
  to side.

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6.1 WavesTypes and Properties

• The figure shows a snapshot of such a wave.
• It shows the shape of the Slinky at some instant
  in time.
• Note that the wave has the same sinusoidal shape
  youve seen before.

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6.1 WavesTypes and Properties

• The high points of the wave are called peaks or
  crests, and the low points are called valleys or
  troughs.
• The straight line through the middle represents
  the equilibrium configuration of the mediumits
  shape when there is no wave.

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6.1 WavesTypes and Properties

• In addition to wave speed, there are three other
  important parameters of a continuous wave that
  can be measured
• amplitude, wavelength, and frequency
• At any moment, the different particles of the
  medium are generally displaced from their
  equilibrium positions by different amounts.
• The maximum displacement is called the amplitude
  of the wave.
• Amplitude The maximum displacement of points on
  a wave measured from the equilibrium position.

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6.1 WavesTypes and Properties

• The amplitude is just a distance equal to the
  height of a peak or the depth of a valley, which
  are the same for a pure wave.
• The amplitude of a particular type of wave can
  vary greatly.
• For water waves, it can be a few millimeters for
  ripples to tens of meters for ocean waves.
• When we hear a sound, its loudness depends on the
  amplitude of the sound wave
• Louder sounds have larger amplitudes.

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6.1 WavesTypes and Properties

• Wavelength The distance between two successive
  like points on a wave.
• For example, the distance between two adjacent
  peaks or two adjacent valleys.
• Wavelength is represented by the lowercase Greek
  letter lambda (l).

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6.1 WavesTypes and Properties

• There is also a large variation in the
  wavelengths of particular types of waves.
• The wavelengths of sound (in air) that can be
  heard by humans range from about 2 centimeters
  (very high pitch) to about 17 meters (very low
  pitch).
• Typical wavelengths for radio waves are 3 meters
  for FM stations and 300 meters for AM stations.

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6.1 WavesTypes and Properties

• Any segment of a wave that is one wavelength long
  is called one cycle of the wave.
• As each cycle of a wave passes by a given point
  in the medium, that point makes one complete
  oscillationup, down, and back to the starting
  position.
• The figure shows three complete cycles of a wave.

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6.1 WavesTypes and Properties

• Amplitude and wavelength are independent features
  of a wave
• A short-wavelength wave can have a small or a
  large amplitude.

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6.1 WavesTypes and Properties

• To understand what the frequency of a wave is, we
  must unfreeze the wave and imagine it as it
  moves along.
• The rate at which the wave cycles pass a point is
  the frequency of the wave.
• Recall that the unit of measure of frequency is
  the hertz (Hz).
• Frequency The number of cycles of a wave
  passing a point per unit time.
• The number of oscillations per second in the wave.

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6.1 WavesTypes and Properties

• If you move the end of a Slinky back and forth
  three times each second, you will produce a wave
  with a frequency of 3 hertz.
• The note A above middle C on a modern piano has a
  frequency of 440 hertz.
• This means that 440 cycles of the sound wave
  reach your ear each second.
• The piano wires producing the sound and the air
  molecules in the room all vibrate with the same
  frequency 440 hertz.

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6.1 WavesTypes and Properties

• Under ideal conditions, a person with good
  hearing can hear sounds with frequencies as low
  as 20 hertz or as high as 20,000 hertz.
• Frequency is important in other kinds of waves as
  well.
• Each radio station broadcasts a radio wave with a
  specific frequencyfor example
• 1,100 kilohertz 1,100,000 hertz, or
• 92.5 megahertz 92,500,000 hertz.

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6.1 WavesTypes and Properties

• Amplitude, wavelength, and frequency can be
  identified for both transverse waves and
  longitudinal waves, although the amplitude of a
  longitudinal wave is a bit difficult to
  visualize.
• It is still the maximum displacement from the
  equilibrium position, but in this case the
  displacement is along the direction the wave is
  traveling.

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6.1 WavesTypes and Properties

• The figure shows a closeup of a Slinky with no
  wave and then with a longitudinal wave traveling
  on it.
• The amplitude is the farthest distance that any
  coil is displaced to the right or left of its
  equilibrium position.

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6.1 WavesTypes and Properties

• The regions where the coils are squeezed together
  are called compressions, and the regions where
  they are spread apart are called expansions or
  rarefactions.
• The wavelength is the distance between two
  adjacent compressions or two adjacent expansions.

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6.1 WavesTypes and Properties

• The speed of a wave, its wavelength, and its
  frequency are related to each other in a simple
  way.
• Imagine a continuous wave passing by a point,
  perhaps ripples moving by a plant stem.
• The speed of the wave equals the number of cycles
  that pass by each second multiplied by the length
  of each cycle.

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6.1 WavesTypes and Properties

• For example, if five cycles pass the stem each
  second and the peaks of the ripples are 0.03
  meters apart, the wave speed is 0.15 m/s.

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6.1 WavesTypes and Properties

• In general,
• wave speed
• number of cycles per second length of each
  cycle
• The two quantities on the right of the equal sign
  are the frequency of the wave and the wavelength,
  respectively.
• Therefore,
• The velocity of a continuous wave is equal to the
  frequency of the wave times the wavelength.

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6.1 WavesTypes and Properties

• In many cases, all waves that travel in a
  particular medium have the same speed.
• Wave pulses, low-frequency continuous waves, and
  high-frequency continuous waves all travel with
  the same speed.
• Sound is an important example of this sound
  pulses, low-frequency sounds, and high-frequency
  sounds travel through the air with the same
  speed,
• 344 m/s at room temperature

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6.1 WavesTypes and Properties

• Similarly, light, radio waves, and microwaves
  travel with the same speed in a vacuum
• 3108 m/s.
• According to the equation v fl, when the wave
  speed is the same for all waves, higher frequency
  waves must have proportionally shorter
  wavelengths.
• A 20-hertz sound wave has a wavelength of about
  17 meters, whereas a 20,000-hertz sound wave has
  a wavelength of about 1.7 centimeters.

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6.1 WavesTypes and PropertiesExample 6.3

• Before a concert, musicians in an orchestra tune
  their instruments to the note A, which has a
  frequency of 440 hertz.
• What is the wavelength of this sound in air at
  room temperature?
• The speed of sound at this temperature is 344
  m/s, so
• The wavelength of sound with a frequency of 220
  hertz is twice as large 1.56 meters.

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6.1 WavesTypes and Properties

• Not all continuous waves have the simple
  sinusoidal shape shown in the figure below.
• In fact, waves with precisely that shape are
  relatively rare.
• Any continuous wave that does not have a
  sinusoidal shape is called a complex wave.

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6.1 WavesTypes and Properties

• The figure shows two examples.
• Note that there are three different-sized peaks
  in each cycle of the upper wave.
• The shape of a wave is called its waveform.
• The two complex waves in the figure have about
  the same wavelength and amplitude, but they have
  very different waveforms.

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6.1 WavesTypes and Properties

• The waveform is another feature that is needed
  when comparing complex waves.

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Concept Map 6.1