Page:Ueber das Doppler'sche Princip.djvu/1

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On the Principle of Doppler.
By
W. Voigt.


It is known that the differential equations for the oscillations of an elastic incompressible medium read:

1)

where ω is the propagation velocity of the oscillations - or more precisely the propagation velocity of plane waves with constant amplitude. It is presupposed that u, v, w fulfill the relation:

1')

Now let u = U, v = V, w = W be solutions of these equations, which on a given surface adopt given values , , which depend on time, then we can say that these functions U, V, W represent the law by which the surface f = 0 is illuminating.