26. EMERGENCE
OF DOPPLER SHIFT EQUATIONS DURING THE
EMISSION OF
AN ELECTROMAGNETIC WAVE
Now that Doppler Shift occurs at
the moment of signal emission and at
the source, then let’s see this occurrence on a graphics first and then
see whether Doppler Shift equations emerged mathematically or not.
Let’s assume
that the factory setting of the signal
transmitter is f0 for the frequency and λ0
for the wavelength. Let’s discuss a piece of the signal that set out
from the transmitter, which is one wavelength long. Since the signals
went to three different targets, the wavelengths of these signals that
went to three targets were formed differently. On the other hand,
although the wavelengths of the signals that are emitted, the fact that
the frequency doesn’t change means that the durations of the emissions
of the signals over λ0, λ1, λ2
wavelengths are equal. We can get the duration of the wavelength
emission from the factory settings of the transmitter. This duration is
λ0/ c = t0. When we multiply the
difference between the reference systems that lead to the formation of
Doppler, namely “v”, with the duration of the wavelength emission “t0”,
we find the amount that leads to the change in the wavelengths of the
signals that go to targets that are in motion.
On the other hand, the
wavelength is a physical quantity, a length, a
distance. Even though their lengths are different, emission of signal
wavelengths that go to three different targets in the same duration of
time directly gives the speeds of the signals that go to targets that
are in motion, as well. And this is clear information.
Since ;
The speed of the signal that goes to the plane that is
moving away =
The speed of the signal that goes to the plane that is approaching =
Consequently, we get: c1 > c > c2
Let’s see if we can get Doppler equations by making use of the figure
above. We can do it easily as can be seen below.

As
we mentioned before, the terms Red Shift and Blue Shift in Doppler
Shift are used to express the increase and decrease in the energy of
the electromagnetic wave. Red Shift is lengthening of the wavelength of
the electromagnetic wave; it indicates a decrease in the energy and is
represented by (c+v). Blue Shift is shortening of the wavelength of the
electromagnetic wave; it indicates an increase in the energy and is
represented by (c-v).