Image 1 Caption: An animation illustrating traveling waves.
The animation helps to illustrate the Doppler effect in a medium at rest in an inertial frame in the classical limit: i.e., when relativistic effects are negligible.
The classical Doppler effect is a shift in frequency depending on the motion of an observer relative to a medium at rest in an inertial frame in the classical limit: i.e., when relativistic effects are negligible. For the same conditions, there is also a shift in wavelength depending on the motion of a source relative to a medium with the source having a fixed emission frequency: i.e., one independent of the source velocity.
Features:
f_2 = f_1[(1 - v_2/v_ph)/(1 - v_1/v_ph)] .
f_2 - f_1 = -f_1(v_2 - v_1)/v_phor in the simplifed relative Doppler shift formula form
Δf/f = -Δv/v_ph ,where Δf is the change in frequency, f is either f_1 or f_2 or an average of these since which is used does NOT matter to 1st order and Δv = (v_2 - v_1) is the relative velocity between the observers.
Note only to 1st order does the Doppler shift depend only on the relative velocity and NOT on v_1 and v_2 individually.
For EMR, wavelength depends on the observer velocity. It is the vacuum light speed is invariant for ALL observers: i.e., they all measure the same invariant NO matter how they are moving.
Similarly,
wavelength is
decreased/increased
(blueshift/redshift
or scrunched/stretched)
in the forward/backward direction
from the car relative
to the car
at rest.
However, one still needs
formulae
for know quantitative behavior and to bring out the
distinction between
frequency
and wavelength
behavior for the classical
Doppler effect.
We present the formula for
the frequency
Doppler shift above.
We present the formula for
the wavelength
Doppler shift below.
Rewriting the last equation, we have
Note all observers in the
medium
measure the same invariant
wavelength
and no one measures
λ_source, unless v_source = 0 in which case
λ = λ_source and all observers in the
medium
measure λ_source.
λ = λ_source(1-v_source/v_ph) .
Δλ/λ_source = -v_source/v_ph ,
where Δλ = λ - λ_source.