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Coupled Oscillators and Wave Equations in Physics

Explore the concepts of coupled oscillators, transverse and longitudinal waves, and wave equations in physics. Learn about wavelength, frequency, and speed of traveling waves. References to fundamental physics theories included.

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Coupled Oscillators and Wave Equations in Physics

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  1. 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

  2. PHY238YLecture 4 • Coupled oscillators • Parallel oscillation: • Symmetric oscillation • See Lecture Notes

  3. 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

  4. PHY238YLecture 4 • Many coupled oscillators: the mass-spring transmission line: • See Lecture notes

  5. PHY238YLecture 4 • The mass-spring transmission line: very many masses and springs. • Displacement of mass number “n” from equilibrium position is ξn :

  6. 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.

  7. 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

  8. 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

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