PHY238Y Lecture 4

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PHY238YLecture 4

• Coupled oscillators
• Many coupled oscillators
• From oscillators to waves
• Transverse and longitudinal waves
• Wavelength and frequency of a wave
• Speed of a traveling wave
• References
• Lecture notes
• Halliday/Resnick/Walker Fundamentals of Physics,
  6th ed., Chapter 17 (17.1 17.5)
• Thanks to dr. R. Nave for the permission to use
  some of the pictures from Hyper Physics
  http//hyperphysics.phy-astr.gsu.edu

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PHY238YLecture 4

• Coupled oscillators
• Parallel oscillation
• Symmetric oscillation
• See Lecture Notes

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PHY238YLecture 4

• Example for Lecture 4
• Infrared spectroscopic data show that sodium
• chloride (NaCl) has an inter-atomic oscillation
• frequency of 1.4 ? 1013Hz.
• Find the inter-atomic force constant (k),
• assuming a model of two masses connected by a
• spring.
• We take mCl 35?1.67?10 -27 kg
• mNa 23?1.67?10 -27 kg
• The model two masses connected by an ideal
  spring

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PHY238YLecture 4

• Many coupled oscillators the mass-spring
  transmission line
• See Lecture notes

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PHY238YLecture 4

• The mass-spring transmission line very many
  masses and springs.
• Displacement of mass number n from equilibrium
  position is ?n

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PHY238YLecture 4

• The Wave Equation
• The wave equation for a plane wave traveling in
  the x direction is
• where v is the phase velocity of the wave and y
  represents the variable which is changing as the
  wave passes. This is the form of the wave
  equation which applies to a stretched string or a
  plane electromagnetic wave.

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PHY238YLecture 4

• Transverse waves displacement is perpendicular
  to the direction of travel
• Longitudinal waves displacement is in the same
  direction as the direction of travel

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PHY238YLecture 4

• Wavelength and frequency
• Periodic motion
• Period the time required to complete a full
  cycle, T in seconds/cycle
• Frequency the number of cycles per second, f in
  1/seconds or Hertz (Hz)
• Amplitude the maximum displacement from
  equilibrium A
• For a traveling wave, one
• needs also
• Velocity of propagation v
• Wavelength repeat distance of wave