Chapter 15 Waves

1
Chapter 15 - Waves

• Traveling Waves
• Types
• Classification
• Harmonic Waves
• Definitions
• Direction of Travel
• Speed of Waves
• Energy of a Wave
• Standing Waves
• Reflection and Transmission
• Superposition and Interference
• (Refraction and Refraction)

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Types of Waves

• Mechanical Waves - Those waves resulting from the
  physical displacement of part of the medium from
  equilibrium.
• Electromagnetic Waves - Those wave resulting from
  the exchange of energy between an electric and
  magnetic field.
• Matter Waves - Those associated with the
  wave-like properties of elementary particles.

3
Requirements for Mechanical Waves

• Some sort of disturbance
• A Medium that can be disturbed
• Physical connection or mechanism through which
  adjacent portions of the medium can influence
  each other.

4
Classification of Waves

• Transverse Waves - The particles of the medium
  undergo displacements in a direction
  perpendicular to the wave velocity
• Polarization - The orientation of the
  displacement of a transverse wave.
• Longitudinal (Compression) Waves - The particles
  of the medium undergo displacements in a
  direction parallel to the direction of wave
  motion.
• Condensation/Rarefraction

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Waves on the surface of a liquid
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3D Waves
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Sound Waves
http//www.kettering.edu/drussell/Demos/waves/wav
emotion.html
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Harmonic Waves

• Transverse displacement looks like

9
Let the wave move
10
Standing at the origin

• Transverse displacement looks like

T
Dm
11
Phase Velocity

• Wave velocity is a function of the properties of
  the medium transporting the wave

12
That negative sign

• Wave moving right
• Wave moving left

13
Alternate notation
Wave number
Angular frequency
14
Definitions

• Amplitude - (A, ym) Maximum value of the
  displacement of a particle in a medium (radius of
  circular motion).
• Wavelength - (l) The spatial distance between any
  two points that behave identically, i.e. have the
  same amplitude, move in the same direction
  (spatial period)
• Wave Number - (k) Amount the phase changes per
  unit length of wave travel. (spatial frequency,
  angular wavenumber)
• Period - (T) Time for a particle/system to
  complete one cycle.
• Frequency - (f) The number of cycles or
  oscillations completed in a period of time
• Angular Frequency - (w) Time rate of change of
  the phase.
• Phase - (kx - wt) Time varying argument of the
  trigonometric function.
• Phase Velocity - (v) The velocity at which the
  disturbance is moving through the medium

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Velocity of transverse wave in a cord
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General rule for wave speeds
Longitudinal wave in a long bar
Longitudinal wave in a fluid
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Superposition

• Waves in the same medium will add displacement
  when at the same position in the medium at the
  same time.
• Overlapping waves do not in any way alter the
  travel of each other (only the medium is effected)

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Superposition in reverse

• Fouriers Theorem any complex wave can be
  constructed from a sum of pure sinusoidal waves
  of different amplitudes and frequencies

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Interference (Superposition of equal amplitude
waves)
Constructive
Destructive
http//www.kettering.edu/drussell/Demos/superposi
tion/superposition.html
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Interference of harmonic waves

• Destructive - Waves are 180 degrees out of phase.
  Amplitude cancellation occurs

• Constructive - Waves are in phase. Amplitude
  doubling occurs

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Reflection
Fixed Boundary Flips
Free Boundary Doesnt flip
http//www.kettering.edu/drussell/Demos/reflect/r
eflect.html
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Standing Waves - Resonance
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Nodes and Antinodes

• Node position of no displacement
• Antinode position of maximum displacement

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Natural frequencies
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Energy in a Wave
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Intensity
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Two dimensional wave reflection