Waves

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Waves
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Wave Properties

• Waves are propagated by a vibrating source
• Pulse single disturbance created by a single
  oscillation
• Periodic Wave periodic disturbance created by a
  continuously vibrating source

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Definition

• Mechanical Wave - transfer of energy through a
  medium
• Waves can move over large distances, but the
  particles of the medium only vibrate about fixed
  positions
• Waves transport energy but not matter
• Mechanical waves must travel through a medium

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Types of Waves

• Transverse particles in medium vibrate
  perpendicular to the direction of the wave motion

crest
A
trough
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• Crest max displacement
• Trough minimum displacement
• ? wavelength distance between two successive
  crests (or troughs)
• A amplitude maximum displacement from the
  rest position

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Longitudinal Waves

• Particles vibrate parallel to the direction of
  wave motion

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• Compression wave particles are compacted
  closely together
• Rarefaction where particles are spread out
• Wavelength distance between two corresponding
  in phase points
• Amplitude maximum displacement from rest

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Damping

• Initial amplitude of the wave depends on the
  initial energy of the source
• Energy decreases over time, so the amplitude does
  as well - damping

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Wave Equation

• The velocity of a wave is related to its
  wavelength and frequency
• Velocity speed the wave travels
• Frequency number of cycles that pass a given
  point per second (in Hertz)
• - measured by crests per second
• v ?f

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Example

• A wave has a wavelength of 5m and a frequency of
  3 Hz. What is its speed?
• A crest of a wave in a pool takes 2.5sec to
  travel from one end to the other end (20m). It is
  noticed that 10 crests pass by a mark in 15 sec.
  What is the wavelength?

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• The frequency of a wave is determined by the rate
  that the source produces them
• The velocity of a wave depends on the properties
  of the medium

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Velocity of Transverse

• In transverse waves the velocity depends on the
  tension (tightness) of the medium and the
  mass/length of the medium
• Greater tension increase both v and f
• v v(Ft/(m/L))

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Example

• A wave of wavelength .30m is traveling down a
  300m long wire of mass 15kg. If the wire is under
  a tension of 1000N, what is the velocity and
  frequency of the wave?

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Longitudinal Velocity

• Velocity in longitudinal waves depends on the
  elasticity(E) of the material and the density(?)
  of the material
• v v(E/ ?)

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Example

• You can hear a train approaching by putting your
  ear to the track. How long does it take for a
  sound wave to travel 1.0km down a steel track?
  E 2.0x1011 N/m2 and ?
  7.8x103 kg/m3