Waves

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Waves

• A wave is a disturbance that carries energy from
  one place to another.

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Waves

• Waves can transfer energy without a large scale
  transfer of matter. Waves may move matter up and
  down, such as in water waves, but not forward.
• Examples of Waves
• dropping a stone in water
• explosion
• sonic boom
• visible light

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Two Types of Waves

• Electromagnetic - a wave that does not need a
  medium (any type of matter) to travel through.
  Consists of changing electric and magnetic fields
  that carry energy from one place to another
• Example Light waves

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Two Types of Waves
Mechanical Waves a disturbance in matter that
carries energy from one place to another. It is
a wave that does need a medium to travel
through. Example sound waves, water waves
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Mechanical Waves

• To generate mechanical waves, a source of energy
  is necessary to cause a disturbance and an
  elastic medium is required to transmit the
  disturbance.
• The elastic medium can be anything that has the
  potential to move. Solids, liquids, gases, etc.

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Three Types of Mechanical Waves

• 1. Transverse - wave pulse moves perpendicular to
  the direction of motion of the wave

Direction of Propagation
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Transverse Wave
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Characteristics of Transverse Waves
wavelength
crest
amplitude
trough
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Characteristics of Transverse Waves

• Crest - highest point in a wave (positive
  displacement)
• Trough - lowest point in a wave (negative
  displacement)
• Amplitude - distance from equilibrium to crest or
  trough
• Wavelength - distance from one crest (or trough)
  to another
• Period - the time it takes for one complete cycle
  of a wave (crest and trough) to pass a
  given point

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Three Types of Mechanical Waves

• 2. Longitudinal - wave pulse moves back and forth
  through medium

compression
rarefaction
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Longitudinal Wave
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Longitudinal Waves

• Instead of positive and negative displacements,
  the elastic medium is compressed and transfers
  energy in that method.
• Compression - where the molecules of a medium are
  pushed together
• Rarefaction - where the molecules of a medium are
  spread out.
• Examples sound waves, sonic boom, explosion

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Three Types of Mechanical Waves

• 3. Surface Waves - a wave that travels along a
  surface separating two media (two types of
  substances)
• Example on top of the ocean (air/water)

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Surface Wave
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Properties of Mechanical Waves

• All waves exhibit periodic motion, which means
  that the motion repeats itself over and over
  again.
• The time for one complete cycle is called the
  Period.
• The number of times it repeats in one second is
  called the frequency.

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Frequency of a Wave

• The frequency of a wave is the number of crests
  (or troughs) that pass a point in 1 second.
  Frequency is measured in Hertz (Hz).
• f Hz 1/s or s-1
• A wave generated at 60 cycles per second has a
  frequency of 60 Hz.

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Period of a Wave

• The period (T) of a wave is the time it takes for
  two successive crests (or troughs) to pass a
  given point. It is related to the frequency by
• f 1/T and T 1/f

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Wavelength

• The wavelength of a wave is represented by ?, the
  Greek letter lambda. ? is the distance between
  any particle on a wave and the nearest particle
  in phase with it. This is measured in meters.
  Increasing the frequency of a wave decreases its
  wavelength.

?
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Wave Speed

• Each wave has a finite speed, v, for a
  transmitting medium. This can be slow as in
  visible waves (water waves) or as fast as light
  waves, c 3x108 m/s.
• The speed of a wave depends on the nature of the
  wave disturbance and on the medium through which
  it passes.

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Wave Speed

• In certain media, wave speed may also depend on
  wavelength.
• This type of media is called disperse.
• Example Glass dispersing light waves, water
  droplets
• Wave speed (frequency)(wavelength)
• v f?

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Amplitude and Energy

• Amplitude the maximum displacement of the medium
  from its rest position.
• Energy needs to be transmitted from object to
  object to create or sustain a wave.
• The more energy a wave has, the greater its
  amplitude.
• The energy expended per unit time determines the
  amplitude, frequency, and the mass of the
  particles of the medium at the source.
• Assuming no losses of energy, the energy of the
  advancing wave is the same as it is at the
  source.

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Amplitude and Energy

• The amount of vibration energy can be increased
  by increasing either the amplitude OR frequency
• Double Amplitude Quadruple Energy
• Double Frequency Quadruple Energy
• The rate of transfer of energy, or the power
  transmitted by a wave system, is directly
  proportional to the square of the wave amplitude
  and also to the square of the wave frequency.

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Damping

• The reduction of amplitude of a wave due to
  dissipation of wave energy as it travels away
  from the source is called damping.

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Behavior of Waves

• Reflection
• Refraction
• Interference
• Diffraction

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Reflection

• Reflection occurs when a wave bounces off of a
  medium instead of being transmitted (passing
  through a medium).

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Two types of reflection

• Total Reflection - all of a wave is reflected
  from the surface of a medium

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Two types of reflection

• Partial Reflection - only some of the wave is
  reflected while the rest is transmitted

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Law of Reflection

• Angle of Incidence Angle of Reflection

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Law of Reflection

• Incident Ray - incoming ray
• Reflected Ray - wave that has been reflected (or
  bounced off of) an object
• Normal - a line that has been drawn perpendicular
  to the surface of an object
• Angle of incidence/reflection - the angle,
  measured in degrees, from the normal to either
  the incident or reflected ray

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Refraction

• Refraction is the bending of a wave as it passes
  from one medium into another, such as air into
  water.
• Refraction occurs due to the different densities
  of the media. The wave will travel different
  velocities in each medium and this will cause the
  waves to bend.
• Sound waves can be refracted just as light waves
  are.

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Refraction
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Diffraction

• The spreading of a wave disturbance beyond the
  edge of a barrier.
• This occurs in one medium, not two as in
  refraction.

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Diffraction
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Interference of Waves

• Waves do not occur one at a time in nature. They
  combine and interference occurs. This
  interference can be either constructive or
  destructive.
• Constructive when two or more waves combine to
  produce a wave with a larger displacement
• Destructive when two or more waves combine to
  produce a wave with a smaller displacement.

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Principle of Superposition

• When two more waves travel simultaneously through
  the same medium, (1) each wave proceeds
  independently as though no other waves were
  present and (2) the resultant displacement of any
  particle at a given time is the vector sum of the
  displacements that the individual waves acting
  alone would give it.

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Principle of Superposition
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Constructive Interference

• Two or more waves overlap and the crests (or
  troughs) of the waves combine and build on one
  another, making a larger amplitude.

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Destructive Interference

• The crest of one wave and the trough of another
  combine and cancel each other out.

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Interference
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Interference Patterns

• Interference patterns are set up when two or more
  waves interact. Points of zero displacement are
  called nodes The lines along which they occur are
  called nodal lines. Points of maximum
  displacement are called antinodes and the lines
  along which they occur are called antinodal lines.

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Nodal / Antinodal Lines
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Wave Interference Patterns
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Standing Waves

• Particles in a standing wave vibrate in simple
  harmonic motion with the same frequency as each
  of the component waves.
• A standing wave is produced by the interference
  of two periodic waves of the same amplitude and
  wavelength traveling in opposite directions.

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Standing Waves

• Nodes are parts of the vibrating string that do
  not move from their equilibrium position

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Nodal / Antinodal Lines
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Sound and Hearing

• Sound waves are longitudinal waves.
• Many behaviors of sound can be explained using a
  few properties - speed, intensity and loudness,
  and frequency and pitch.

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Sound

• All sounds are produced by the vibrations of
  material objects.
• The vibration of the material vibrates the air
  around it at the same frequency which produces
  longitudinal waves.
• Vibrations occur at all frequencies, but we can
  only hear from 20 Hz - 20,000 Hz.

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Sound

• Loudness of sound is subjective What is loud to
  one person may not be to another.
• Loudness is based on a logarithmic scale known as
  decibels (dB).

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Decibel Scale

• Source of Sound dB
• Jet engine at 30 meters 140
• Threshold of Pain 120
• Loud Rock Music 115
• Normal Speech 60
• Close Whisper 20
• Normal Breathing 10
• Threshold of Hearing 0

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Ultrasound

• Ultrasound is the set of frequencies above what
  people can hear (20,000 Hz )
• Ultrasound is used in a variety of applications,
  including sonar and ultrasound imaging.
• Sonar - SOund NAvigation and Ranging

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The Doppler Effect

• The frequency of sound that an object emits will
  appear to change as the object nears or gets
  farther from an observer. The faster the object
  moves, the greater the change in frequency (or
  pitch).
• Examples
• A racecar traveling around a track
• A passing train blowing a horn
• Police RADAR

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The Doppler Effect

• Sound emitted by a stationary observer moves
  outward in all directions with the same
  wavelength.

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The Doppler Effect

• If the object emitting the sound moves toward
  you, the object pushes the waves together,
  shortening the wavelength and raising the pitch

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The Doppler Effect

• As the object pulls away from you, the waves are
  pulled or spread out, increasing the wavelength
  and lowering the pitch.

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The Doppler Effect
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The Doppler Effect

• The Doppler Effect also occurs when an observer
  is moving and object emitting the sound stays in
  the same location.
• The Doppler Effect also happens with light waves.
  When a light source approaches, the wavelength
  shortens, and it is called a blue shift. When an
  object moves away, the wavelength increases and
  it is called a red shift.
• This is how scientists measure the speed and
  direction of galaxies and stars.

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The Speed of Sound - Mach 1
Speed 340m/s or 750 mph
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Hearing and the Ear

• The outer ear gathers and focuses sound into the
  middle ear, which receives and amplifies the
  vibrations. The inner ear uses nerve endings to
  sense vibrations and send signals to the brain.

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How sound is reproduced

• Sound is recorded by converting sound waves into
  electronic signals that can be processed and
  stored. Sound is reproduced by converting
  electronic signals back into sound waves.

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Music

• Most musical instruments vary pitch by changing
  the frequency of standing waves, causing
  resonance.
• When striking an object, a vibration occurs. If
  this vibration matches the natural frequency of
  an object, a dramatic increase in amplitude
  occurs which is called resonance.
• Example English infantry troops marching across
  a footbridge in 1831 inadvertently caused the
  bridge to collapse when they marched in rhythm
  with the bridges natural frequency. Since then,
  it is customary for troops to break step when
  crossing bridges.

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