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:
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.
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).
(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.
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.