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Superposition - PowerPoint PPT Presentation


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Superposition. Principle of Superposition If two or more waves occupy the same position at the same time, then the waves combine to form a new wave. The resulting wave has an amplitude that is the algebraic sum of the individual waves at that point.

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superposition
Superposition
  • Principle of Superposition
    • If two or more waves occupy the same position at the same time, then the waves combine to form a new wave. The resulting wave has an amplitude that is the algebraic sum of the individual waves at that point.
slide2
Distinguishes between particle mechanics and wave mechanics
    • Particles never occupy the same position at the same time, nor do they obey the Principle of Superposition.
    • Waves can occupy the same position at the same time, and they obey the Principle of Superposition
equation for wave
Equation for wave
  • Can use Principle of Superposition to find equation for waves.
    • Require wave to be periodic in time with cell size given by period
    • Require wave to be periodic in space with cell size given by wavelength.
    • Wave’s velocity must satisfy v = fl.
    • Start with form y(x,t) = A sin(ax-bt)
temporal periodicity
Temporal periodicity
  • Periodicity in time yields
  • Require both sides to be equal for any x, so
spatial periodicity
Spatial periodicity
  • Periodicity in position yields
  • Require both sides to be equal for any t, so
speed of wave
Speed of wave
  • Define the wave number, k, to be
  • Recall that
  • Equation of wave is thus
slide7
Assume peak at time t = 0 is at x = 0. Then
  • (-) in trig argument -> movement in (+) direction
  • (+) in trig argument -> movement in (-) direction