EXPERIMENTS IN PHYSICS WITH DR. FRANK OPPENHEIMER

Program 7: Wave and Group Velocity.

Two audio-oscillators are used in conjunction with a dual-trace oscilloscope. The output of audio-oscillator I triggers the sweep on channel I. The frequency of audio-oscillator II can be set almost equal to that of audio-oscillator I, or at frequencies above and below this which give a clean wave pattern on the face of the scope. A fine adjustment of the frequency of oscillator II will make the wave pattern move with a measurable velocity across the face of the scope. This one wave moves with the phase velocity u = 0, and the other wave will move with a velocity u + du. It is possible to measure lamda, the wavelength of both waves, and therefore delta-lamda. From this information it is possible to calculate the velocity of the group which is formed when both waves are added. It is, of course, also possible to measure this velocity and compare the two values. By examining carefully the pattern which occurs when both waves are displayed simultaneously, but not added, it is possible to see why the group velocity is different from that of the phase velocity. By using a very slow sweep rate, one can show that the more familiar phenomena of beats is really that of a very long group passing by the observer.



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