- Qualitatively, the
animation
explains much of the behavior.
Along the car,
frequency
is increased/decreased
(blueshift/redshift)
in the forward/backward direction
from the car relative
to the car
at rest.
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 formulae below.

- Inside the car,
the observer and the source
are at rest
relative to the
medium.
So the inside observer, just measures
instrinsic source frequency f_source
and
intrinsic source wavelength
### λ=v_ph/f_source ,

where v_ph is the phase velocity of the medium (i.e., the wave propagation velocity observed when the observer is at rest in the medium). The formula follows from the general phase velocity formula fλ=v_ph. - An outside observer moving with
the car
still measures intrinsic source
frequency f_source.
- An outside observer at rest
in the medium
on the path of the car motion observes
f_source f= ------------- , (1 - v_1/v_ph)

where v_1 is measured positive/negative if your are**AHEAD/BEHIND**of the car.A bit more precisely if trickily, v_1 is measured positive/negative for wave propagation with/opposite the direction of car motion.

If v_1 is positive/negative, there is a increase/decrease in frequency from f_source to f (i.e., there is a blueshift/redshift).

- An outside observer moving at
velocity v_2
on the path
of the car motion observes
(1 - v_2/v_ph) f_2 = f_source -------------- , (1 - v_1/v_ph)

where v_2 is measured positive/negative for wave propagation with/opposite the direction of observer motion.Note if v_2 = v_1, then the observer just measures f_source.

- All outside observers
on the path of the car motion
no matter how they are moving observe
### λ = λ_source(1-v_1/v_ph) ,

where v_1 is measured positive/negative for wave propagation with/opposite the direction of car motion.The fact that λ is independent of observer motion is because in the classical limit, length (i.e., the distance between 2 points at one instant in time) is independent of the motion of the observer. This is a tricky point about the classical Doppler effect.

- Note that a
blueshift is often considered
just as a
negative
redshift.
- The classical Doppler effect
formulae given above
are derived and further explicated in
file
doppler_effect_classical_derivation.html.

Caption: An animation showing the classical (i.e., non-relativistic) Doppler effect for sound for a siren from a car at rest and in motion relative to the air.

The classical Doppler effect is a shift in frequency depending on the motion of an observer relative to a (transmission) medium and a shift in wavelength depending on the motion of a source with a fixed emission frequency: i.e., one independent of the source velocity.

Features:

Image link: Wikipedia: File:Dopplerfrequenz.gif.

Local file: local link: doppler_effect_siren_animation.html.

File: Waves file: doppler_effect_siren_animation.html.