Waves

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Waves
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Wave

• Wave a rythmic disturbance (oscillation) in both
  time and space.
• Waves transfer energy not matter.
• High amplitude- high energy.
• Low amplitude- low energy.

Simulation Traveling Waves http//higheredbcs.wi
ley.com/legacy/college/halliday/0471320005/simulat
ions6e/index.htm?newwindowtrue
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Vibration in Time
Speed vd/t
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Vibration in Space
l
Speed v d/t l/T lf
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Speed of a Wave

• v d/t
• v l/T
• v lf

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Wave Categories

• Mechanical Waves require a medium.
• Examples
• Water waves( Tsunami)
• Sound waves (f20-20000 hertz, v 340 m/sec in
  air but varies for different media, faster in
  solids)
• Earthquake waves
• Electromagnetic Waves do not require a medium.
  Can travel through space (vacuum).
• Example Light from the sun reaches us
• Note all EM waves have a speed through vacuum of
  3 x 108 m/sec.

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Transverse Waves

• The particles vibrate perpendicular to the
  direction of the wave's propagation
• (ex waves along a string, electromagnetic
  waves).

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Longitudinal Waves

• The particle displacement is parallel to the
  direction of wave propagation (ex sound)

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Elliptical Waves

• Result when longitudinal and transverse waves
  are superpositioned.
• (ex surface water waves)

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Torsional Waves

• Video link on Web
• http//www.enm.bris.ac.uk/research/nonlinear/tacom
  a/tacnarr.mpg

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Electromagnetic Waves

• Type of radiation Wavelengths(m)
• Radio 570 - 2.8
• TV 5.6 - 0.34
• Microwave 0.1 - 0.001
• Infrared radiation 10-3 - 10-7
• visible light
• red 700x10-9 (700nm)
• orange
• yellow
• green
• blue
• indigo
• violet 400x10-9 (400nm)
• ultraviolet 10-7 - 10-10
• x-rays 10-10 -10-12
• gamma rays shorter than 10-12

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Note

• A waves speed is constant in a given medium.
  Therefore if you change the frequency of the
  wave, the wavelength will also change. If the
  frequency increases, the wavelength will
  decrease.
• When a wave travels from one medium to a
  different medium, the frequency remains the same
  and the speed changes.

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Problem

• What is the distance a sound wave in air traveled
  in 2 sec? Assume the speed of sound to be 340m/s.

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Problem

• A student standing outside, shouts and hear her
  echo 1sec later. How far from the obstacle (wall)
  was she standing?

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Problem

• What is the frequency of a light wave of wave
  length 550x 10-9 m?
• What color light is it?

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Refraction
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Refraction
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Dispersion
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Diffraction
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Interference

• Superposition when two pulses pass the same
  point at the same time the waves superimpose
  either constructively or destructively.
• Simulation Constructive and Destructive
  Interference (string with loose or fixed end)
• http//bcs.wiley.com/he-bcs/Books?actionresource
  bcsId1074itemId0471320005resourceId169

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Standing Waves

• When a continuous wave is sent along a string or
  tube, at certain frequencies a standing wave
  pattern forms due to the superposition of the
  incident and the reflected wave as shown in the
  applet.
• http//bcs.wiley.com/he-bcs/Books?actionresource
  bcsId1074itemId0471320005resourceId169

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Standing Wave on a Fixed End String

• Nodes

Fundamental Frequency (first harmonic)
Second Harmonic
Third Harmonic
Antinodes
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Natural Frequencies of a StretchedString (Fixed
Ends)

• Fundamental Frequency
• First Harmonic

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Problem 1

• A string of length 1m vibrates. The speed of the
  wave in the material is 400m/s.
• Calculate the first three natural frequencies and
  draw the corresponding standing waves.

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Bar with One Fixed and One Open End

• Fundamental (First Harmonic)

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Problem 2

• A metal bar is fixed on one end and free at the
  other. Its length is 50cm and it vibrates. The
  waves speed is 3000m/s. Calculate the first
  three natural frequencies and draw the
  corresponding standing waves.

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