2.3. Doppler's principle - correct relations
In one second a standing source will emit n oscillations of the wavelength
c - the speed of light in the standing medium
During the time of
, the oscillations will be distributed in the distance of
When the source moves away from the observer at speed u the oscillations would "expand" in the distance of
a) When the source approaches to the observer at speed u (sign-u), the oscillations would be compressed in the distance of
Let the observer move against the oscillation at speed v (sign-v).
During the period
, the oscillations would be compressed in the distance of
The frequency would thus be heightened from n to N and it is valid
b) If they both (S and O) move away with regard to the medium, i.e. the case is +v and +u. We get "the expansion" of the wave length both by the source and observer. That is why
Fig. 2.22. Doppler's principle - generally
Fig. 2.23. The transversal Doppler's phenomenon - incorrectly interpreted
The transversal Doppler's phenomenon is incorrectly interpreted in the existing theories - see fig. 2.23.
Fig. 2.24. The source (S) motion along the circle with the observer (O)
Fig. 2.25. Alternately accelerated and decelerated motion along a normal cycloid
The angle between the connecting ine SO(ik) and the direction of motion S(u) is permanently changing in range from several degrees up to . The pure transversal Doppler's phenomenon should occur with the constant angle of , i.e. the source motion along the circle with the observer in its centre (see fig. 2.24). Alternately, accelerated and decelerated motion can occur, along a normal cycloid where it always holds that so that the source speed is not decisive, while is valid,
(see fig. 2.25)
It is possible to materialize this case in such a way that the source will be fastened on the circumference of the circle, the observer will be placed in its centre, while the circle will roll along the straight line and the centre of circle (the observer) will move at speed v.
Fig. 2.26. The transversal Doppler's phenomenon - general
Fig. 2.27. The frequency N - as perceived by the observer, "pulsates" around the source frequency n
Analogically, if S (source) and O (observer) are interchanged, then it holds
Should any such circle roll along any curve (with the source on its circumference and the observer in its centre), the result would be the generally known case pictured in fig. 2.26 and it holds
Analogically, if S and O are interchanged, then it holds
In this way the change of frequency N occurs permanently. The frequency N as perceived by the observer - "pulsates" around the frequency of source n, see fig. 2.27.