Many coupled oscillators From oscillators to waves:

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Presentation transcript:

Many coupled oscillators From oscillators to waves: PHY238Y Lecture 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

Parallel oscillation: PHY238Y Lecture 4 Coupled oscillators Parallel oscillation: Symmetric oscillation See Lecture Notes

PHY238Y Lecture 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

Many coupled oscillators: the mass-spring transmission line: PHY238Y Lecture 4 Many coupled oscillators: the mass-spring transmission line: See Lecture notes

PHY238Y Lecture 4 The mass-spring transmission line: very many masses and springs. Displacement of mass number “n” from equilibrium position is ξn :

PHY238Y Lecture 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.

PHY238Y Lecture 4 Transverse waves: displacement is perpendicular to the direction of travel Longitudinal waves: displacement is in the same direction as the direction of travel

Wavelength and frequency: PHY238Y Lecture 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