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



By W. Voigt.

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

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:

Now let u = U, v = V, w = W be solutions of these equations, which on a given surface $$f(\bar{x},\bar{y},\bar{z})=0$$ adopt given values $$\bar{U}$$, $$\bar{V}$$, $$\bar{W}$$ 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.