Waves and Sound

1
Chapter 6

• Waves and Sound

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Waves types and properties

• A wave is a traveling disturbance consisting of
  coordinate vibrations that transmit energy with
  not net movement of matter.
• The disturbance is frequently called an
  oscillation or vibration.
• The substance through which the wave travels is
  called the medium.

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Waves types and properties, contd

• There are two main wave types
• Transverse waves have oscillations that are
  perpendicular (transverse) to the direction the
  wave travels.
• Examples include waves on a rope, electromagnetic
  waves and some seismic waves.
• Longitudinal waves have oscillations that are
  along the direction the wave travels.
• Examples include sound and some seismic waves.

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Waves types and properties, contd

• This figure illustrates the two main types of
  waves.

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Waves types and properties, contd

• Consider a string of length l and mass m.
• The speed at which a wave travels on the string
  when it is under a tension T is
• r is the mass per unit length

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Waves types and properties, contd

• From this we see that the speed
• Increases as the tension increases.
• The string has a greater restoring force that
  attempts to straighten it out.
• Is faster for smaller strings.
• The string has less mass that has to be moved by
  the restoring force.
• Is independent of the length.
• The speed depends on the mass per length, not on
  just the length.

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ExampleExample 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 in 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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ExampleExample 6.1
ANSWER The problem gives us The linear mass
density is
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ExampleExample 6.1
ANSWER The wave speed is then
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Waves types and properties, contd

• The speed of a sound wave when the air is at a
  temperature T is
• The temperature must be in Kelvin.

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ExampleExample 6.2

• What is the speed of sound in air at room
  temperature (20ºC 68ºF)?

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ExampleExample 6.2
ANSWER The problem gives us We need to convert
this temperature from celsius to kelvin The
sound speed is then
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ExampleExample 6.2

• DISCUSSION
• The factor of 20.1 depends on the properties of
  air.
• For other gases
• Helium
• Carbon dioxide

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Waves types and properties, contd

• The amplitude of a wave is the maximum
  displacement of the wave from the equilibrium
  position.
• It is just the distance equal to the height of a
  peak or the depth of a valley.

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Waves types and properties, contd

• The wavelength is the distance between successive
  like points on a wave.
• Like points might be peaks, valleys, etc.
• The wavelength is denoted by the Greek letter
  lambda l.

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Waves types and properties, contd

• Here is an illustration of changing the
  wavelength and/or amplitude.
• Lower amplitude implies smaller height/depth.
• Shorter wavelength implies more complete waves
  fit in a given distance.

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Waves types and properties, contd

• The frequency of a wave indicates the number of
  cycles of a wave that pass a given point per unit
  time.
• It is the number of oscillations per second.

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Waves types and properties, contd

• We use different terminology for the peaks and
  valleys of a longitudinal wave.
• A compression is where the medium is squeezed
  together.
• A expansion is where the medium is spread apart.

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Waves types and properties, contd

• The wavelength and frequency are related to the
  wave speed according to
• v is the waves speed,
• f is the waves frequency, and
• l is the waves wavelength.

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ExampleExample 6.3

• Before a concert, musicians in an orchestra tune
  their instruments to the note A, which has a
  frequency of 440 Hz. What is the wavelength of
  this sound in air at room temperature?
• The speed of sound at this temperature is 344
  m/s.

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ExampleExample 6.3
ANSWER The problem gives us The relation
between frequency, wavelength and wave speed
is The wavelength is then
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Waves types and properties, contd

• A complex wave is any continuous wave that does
  not have a sinusoidal shape.

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Aspects of wave propagation

• There are two approaches to represent a wave.
• A wavefront is a circle representing the location
  of a wave peak.
• A ray is an arrow representing the direction
  that a wave segment is traveling.

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Aspects of wave propagation, contd

• A reflection is when a wave abruptly changes
  direction.
• A wave is reflected whenever it reaches a
  boundary of its medium or encounters an abrupt
  change in the properties of its medium.

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Aspects of wave propagation, contd

• The Doppler effect is an apparent change in a
  waves wavelength due to the relative motion
  between the source and receiver.
• Consider a source emitting waves and moving to
  the right.
• The crests appear closer together in the
  direction the source moves.

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Aspects of wave propagation, contd

• The crests appear farther apart in the direction
  opposite to the sources motion.
• These changes cause the frequency to sound
  different since the wave travels at the same
  speed relative to the medium.

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Aspects of wave propagation, contd

• Diffraction results whenever a wave has to travel
  past a barrier or obstruction.
• As the wave travels through the opening, the
  outgoing waves bend.
• The amount of diffraction depends on the
  wavelength and the size of the obstruction.

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Aspects of wave propagation, contd

• Diffraction explains why you can hear a sound
  through a door even if youre behind a wall.
• The sounds wavelength is much longer than the
  size of the door, so the sound wave bends
  around the wall.

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Aspects of wave propagation, contd

• Interference occurs whenever two or more waves
  overlap.

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Aspects of wave propagation, contd

• When the waves interfere to create a larger
  amplitude, we call it constructive
  interference.
• When the waves interfere to reduce the
  amplitude, it is called destructive
  interference.

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Sound

• The speed of sound in a substance depends on
• the mass of its constituent atoms, and
• the strength of the forces between the atoms.
• The speed of sound is large when
• the atoms have small mass theyre easier to
  move, and/or
• the forces between the atoms are larger an atom
  pushes harder on its neighbor.

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Sound, contd

• Typically we represent a sound wave as a
  transverse wave (even though it is not).
• A region of compression is drawn as a crest.
• A region of expansion is drawn as a trough.

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Sound, contd

• A waveform of a sound wave is a graph of the
  air-pressure fluctuations causes by the sound
  wave versus time.
• A pure tone is a sound with a sinusoidal
  waveform.
• A complex wave is a sound that is not pure.

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Sound, contd

• Noise is sound that has a random waveform.
• It does not have a definite wavelength or period.
• Sound with frequencies below our audible range is
  called infrasound.
• Below about 20 Hz.
• Sound with frequencies above our audible range is
  called ultrasound.
• Above about 20,000 Hz.

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Production of sound

• Sound can be produced by
• Causing a body to vibrate
• e.g., plucking a string.
• Varying an air flow
• e.g., buzzing your lips.
• Abrupt changes in an objects temperature
• e.g., a lightning flash creates thunder.
• By creating a shock wave
• e.g., flying faster than the speed of sound.

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Production of sound

• A piano produces sound by
• The player presses a key so that the hammer
  strikes the wire.
• The wire vibrates and transmits this vibration
  to the soundboard.
• The soundboard then radiates the sound to the
  room.

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Production of sound

• A flute produces sound by
• The player blows across the opening to create a
  varying airflow.
• The airflow reaches the end of the flute and
  radiates to the room.
• Or the player opens a note-hole to release part
  of the wave.
• The tube is then effectively shortened.

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Perception of sound

• We have to be careful when we discuss sound.
• There are physical properties we can measure.
• But our ears do not just measure these physical
  properties.
• We have to deal with the perception of the sound.

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Perception of sound, contd

• Pitch is the perception of highness or lowness of
  a sound.
• The pitch depends primarily on the frequency of
  the sound.
• It also depends on the duration.
• A very short sound might sound like a click even
  if it has a definite frequency.

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Perception of sound, contd

• Loudness is the perception of whether a sound is
  easy to hear or painful to hear.
• It depends primarily on the amplitude of the
  sound.
• It also depends on whether the sound is played
  with other sounds (before, after, concurrently,
  etc).
• It even depends on the frequency.
• Our ears are more sensitive to higher frequencies
  and less sensitive to lower frequencies.

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Perception of sound, contd

• Our eardrums respond to sound pressure level.
• A louder sound creates a larger compression,
  i.e., higher pressure, than a quiet sound.
• We typically call the sound pressure level just
  the sound level.
• It is measured in decibels (dB).
• 0 dB corresponds to inaudible.
• Normal conversation is about 50 dB.
• 120 dB starts causing pain.

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Perception of sound, contd

• The sound level of the quietest sound is called
  the threshold of hearing.
• The sound level at which we start experiencing
  pain is called the threshold of pain.
• The minimum increase in sound level that is
  noticeable is about 1 dB.
• For a sound to be judged as twice as loud, the
  original sound must be increased by 10 dB.

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Perception of sound, contd

• To make a sound twice as loud, you would need
  ten equal sources.
• Two sounds with equal sound levels cause an
  increase of 3 dB over a single such sound.

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Perception of sound, contd

• Tone quality is a measure by which two sounds of
  the same frequency and amplitude sound different.
• A sax sounds different from a trumpet playing the
  same note because the two instruments have
  different tone qualities.
• We typically refer to tone quality as timbre or
  tone color.

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Perception of sound, contd

• Any complex waveform is equivalent to a
  combination of two or more sinusoidal waveforms
  with definite amplitudes and specific
  frequencies.
• Theses component waveforms are called harmonics.
• The frequencies of the harmonics are
  whole-numbered multiples of the complex
  waveforms frequency.

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Perception of sound, contd

• We can construct the waveform on the left by
  adding the three waveforms (harmonics) on the
  right.

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Perception of sound, contd

• The specific tone quality of a sound depends on
• the number of harmonics that are present, and
• the relative amplitudes of these harmonics.
• A spectrum analyzer displays a complex waveform
  in terms of the constituent harmonics.