Wave Motion and Sound

1
Wave Motion and Sound
2
Waves

• Nature of Waves
• A wave is a disturbance that transfers energy
  from one place to another without requiring any
  net flow of mass.
• mechanical waves require a medium (air, water,
  rock, etc.) in which to travel.
• Light, and other electromagnetic waves, do not
  require a medium we'll deal with those later in
  the semester.
• pulse and periodic waves
• A pulse is a single disturbance
• a periodic wave is a continually oscillating
  motion. There is a close connection between
  simple harmonic motion and periodic waves in
  most periodic waves, the particles in the medium
  experience simple harmonic motion.
• Waves can also be separated into transverse and
  longitudinal waves.
• transverse wave
• the motion of the particles of the medium is at
  right angles (i.e., transverse) to the direction
  the wave moves.
• longitudinal wave
• the particles oscillate along the direction of
  motion of the wave (sound waves )
• Surface waves, such as water waves, are generally
  a combination of a transverse and a longitudinal
  wave. The particles on the surface of the water
  travel in circular paths as a wave moves across
  the surface.

I can ride this wave!
3
Waves

• Types of Waves
• transverse wave
• longitudinal wave

4
Waves

• Periodic Waves
• Cycles or patterns that are produced over and
  over again are called periodic waves

Transverse wave
Snapshot at one time of the slinky
A single point on the slinky
One wave cycle is shaded area
5
Waves

• Nature of Sound
• Sound is a longitudinal wave that is created by a
  vibrating object
• Sound travels by compressing air
• Sound can be transmitted only in a medium such as
  gas, liquid or solid
• No sound in space!
• In general sound travels faster through a more
  dense material
• 4 times as fast through water than air
• Sound Intensity
• Example 6 page 462

6
Waves

• Sound Intensity
• Decibels (dB)
• A measurement unit used for comparing two sound
  intensities (or voltage, power, etc. levels as we
  will see in MP4)
• The human ear has an incredibly large range
• We are able to detect sound intensities from 1 x
  10-12 W / m2 to 1 W / m2.
• A more convenient way to measure the loudness of
  sound is in decibels (dB) in decibels, the range
  of human hearing goes from 0 dB to 120 dB. The
  ear responds to the loudness of sound
  logarithmically, so the decibel scale is a
  logarithmic scale
• On the decibel scale, doubling the intensity
  corresponds to an increase of 3 dB.
• For humans this 3dB increase does not correspond
  to a perceived doubling of loudness
• We perceive loudness to be doubled when the
  intensity increases by a factor of 10. This
  corresponds to a 10 dB increase. A change by 1 dB
  is about the smallest change a human being can
  detect.
• Example 9 page 465

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Waves

• Sound Intensity Decibels (dB) and the ear
• The decibel scale is used because it corresponds
  to how we perceive the loudness of sounds.
• The ear is split into three sections
• the outer ear
• The outer ear acts much like a funnel, collecting
  the sound and transferring it inside the head
  down a passage that's about 3 cm long, ending at
  the ear drum.
• the middle ear
• The middle ear is connected to the mouth via the
  eustachian tubes to ensure that the inside of the
  eardrum is maintained at atmospheric pressure.
  This is necessary for the drum to be able to
  respond to the small variations in pressure from
  atmospheric pressure that make up the sound wave.
  
• In the middle ear are three small bones, called
  the hammer, anvil, and stirrup because of their
  shapes. These transfer the sound wave from the
  ear drum to the inner ear. Similar to a hydraulic
  lift, the pressure is transferred from a
  relatively large area (the eardrum) to a smaller
  area (the window to the inner ear). By Pascal's
  principle, the pressure is constant. The force is
  smaller at the small-area inner ear, but the work
  done at each end is equal, so the inner ear
  experiences a vibration with a much larger
  amplitude than that at the ear drum. The bones,
  in effect, act as an audio amplifier.
• The three bones in the middle ear are designed to
  transfer sound energy from the eardrum to the
  inner ear without any energy lost to reflections.
  The physics term for this is "impedance match"
  any time energy is transferred from one system to
  another without any reflected energy, the
  impedances are matched at the transfer point...in
  this case, the bones provide the impedance
  matching.
• the inner ear
• The inner ear contains a fluid-filled tube, the
  cochlea. The cochlea is coiled like a snail, is
  about 3 mm in diameter, and is divided along its
  length by the basilar membrane. It also contains
  a set of hair cells that convert the sound wave
  into electrical pulses these are transferred
  along nerves to the brain, to be interpreted as
  sound. When a sound signal enters the inner ear,
  a small movement of the basilar membrane or the
  fluid in the cochlea results in the rubbing of
  another membrane across the hair cells. The
  relatively long hairs provide another level of
  amplification, in the sense that a small force
  applied at the ends is converted into a
  relatively large torque

8
Waves

• Doppler Effect
• The Doppler effect describes the shift in the
  frequency of a wave sound when the wave source
  and/or the receiver is moving.
• the Doppler effect applies to any kind of wave.
  As with ultrasound, the Doppler effect has a
  variety of applications, ranging from medicine
  (with sound) to police radar and astronomy (with
  electromagnetic waves).
• If you hear an emergency vehicle with its siren
  on, you notice an abrupt change in the frequency
  of the siren when it goes past you.
• If you are standing still when the vehicle is
  coming toward you, the frequency is higher than
  it would be if the vehicle was stationary
• when the vehicle moves away from you, the
  frequency is lower.

9
Waves

• Doppler Effect
• General case Doppler Effect equation

Vo is observer Vs is source
10
Waves
Doppler blood flow meter. This device measures
the speed of blood flow using transmitting and
receiving elements that are placed on the skin.
The Doppler flow meter can be used to locate
regions where blood vessels have narrowed.

• Doppler Effect
• Real World Applications

NEXRAD weather radar. The color enhanced view of
a tornado shows winds moving toward (green) and
away (red) from a NEXRAD station, which is below
and to the right of the figure. The white dot and
arrow indicate the storm center and direction of
wind circulation
11
Waves

• Interference
• Interference is what happens when two or more
  waves come together
• Depending on how the peaks and troughs of the
  waves are matched up
• the waves might add together or
• they can partially or even completely cancel each
  other. The concept of interference applies to
  sound waves, and all waves.
• Linear Superposition
• when two or more waves come together, the result
  is the sum of the individual waves.
• The principle of linear superposition applies to
  any number of waves
• consider what happens when two waves come
  together. This could be sound reaching you
  simultaneously from two different sources, or two
  pulses traveling towards each other along a
  string. When the waves come together, what
  happens? The result is that the waves are
  superimposed they add together, with the
  amplitude at any point being the addition of the
  amplitudes of the individual waves at that point.
  
• Although the waves interfere with each other when
  they meet, they continue traveling as if they had
  never encountered each other. When the waves move
  away from the point where they came together, in
  other words, their form and motion is the same as
  it was before they came together.

12
Waves

• Interference
• Constructive
• Constructive interference occurs whenever waves
  come together so that they are in phase with each
  other. This means that their oscillations at a
  given point are in the same direction, the
  resulting amplitude at that point being much
  larger than the amplitude of an individual wave.
  For two waves of equal amplitude interfering
  constructively, the resulting amplitude is twice
  as large as the amplitude of an individual wave.
  For 100 waves of the same amplitude interfering
  constructively, the resulting amplitude is 100
  times larger than the amplitude of an individual
  wave. Constructive interference, then, can
  produce a significant increase in amplitude.
• The following diagram shows two pulses coming
  together, interfering constructively, and then
  continuing to travel as if they'd never
  encountered each other.

13
Waves

• Interference
• Destructive
• Destructive interference occurs when waves come
  together in such a way that they completely
  cancel each other out. When two waves interfere
  destructively, they must have the same amplitude
  in opposite directions. When there are more than
  two waves interfering the situation is a little
  more complicated the net result, though, is that
  they all combine in some way to produce zero
  amplitude. In general, whenever a number of waves
  come together the interference will not be
  completely constructive or completely
  destructive, but somewhere in between. It usually
  requires just the right conditions to get
  interference that is completely constructive or
  completely destructive.
• The following diagram shows two pulses
  interfering destructively. Again, they move away
  from the point where they combine as if they
  never met each other.

14
Waves

• Beats
• Periodic variations in amplitude that arise from
  the linear superposition of two waves that have
  slightly different frequencies
• With sound waves the variation in amplitude cause
  the loudness to vary at the beat frequency
• The beat frequency is the difference between the
  2 source frequencies

Yeah, Im a rock star, because I tune my guitar
with BEATS