Herein, we make the substitution according to (10), than we have

This gives for *x = ϰt*:

14') |

thus we have an illuminating plane (moving parallel to the *X*-axes), which oscillates with a wave-length (only different of the second order of *T*). The propagated oscillation can be written:

14) |

Thus we get, within the propagated wave, a reduced period of oscillation in the relation of .

Is the observer is in motion as well, then:

This formula gives the principle of Doppler for plane waves. But it is in no way universal, but essentially presupposes a *plane wave with constant amplitude throughout*.

2) The same plane is to be set in oscillation by the law:

- as it similar occurs when a wave with initially constant amplitude travels through a prism of an absorbing substance - then for the propagated wave it is given: