SUPERPOSITION OF WAVES!

Two or more different waves in the same medium combine algebraically: y(x,t) = y₁(x,t) + y₂(x,t) + …

Two waves moving in the same direction with the same amplitude but different phase speeds, v_p.

Two waves of the same amplitude and frequency moving in opposite directions with the same phase speed produce the phenomenon known as a “standing wave.”

Two waves with the same amplitude and speed but slightly different frequencies produce the amazing and beautiful phenomenon of “beats.”

SOUND BEATS

Any wave pulse or form can be viewed as a superposition of individual sinusoidal waves of various wavelengths. In a dispersive medium, where the phase speed of a wave depends on the wavelength, the speed with which a pulse moves is thus different from any given phase speed. If the phase speed is ω/k, for a given wave in the set, the pulse created by the superposition of the various waves moves with an overall group speed, v_g = dω/dk.  Look at the animation below!


GROUP VELOCITY ANIMATIONS
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