The Doppler Effect

If you have ever noticed that ambulance sirens or car horns change pitch as they pass by on the highway, then you have experienced the Doppler effect.  The Doppler effect is named after Austrian physicist Johann Doppler who first did the analysis for sound in 1842.
When a sound source is stationary, two observers on each side of it hear the same pitch of sound.
When the source is moving from one observer to the other, as shown below,  then the person it is moving toward hears a higher pitch than the person it is moving away from.  The observer on the left hears a lower tone than the observer on the right.

If the observer is moving instead of the source, the same effect occurs.  When the observer moves toward the source, the frequency increases.  When the observer moves away, the frequency decreases.  When both the source and the observer are moving, then the resulting frequency heard by the observer depends on both the velocity of the observer and the velocity of the source.  If they are moving at the same velocity, then no change is heard.

The frequency that is heard when the source is in motion can be determined by the equation:

f ' = (1/ (1 ± vs/v))f

where f ' is the heard frequency, vs is the source velocity,
v is the velocity of the wave, and f is the frequency of the wave.

The frequency that is heard when the observer is moving can be expressed as:

f ' = (1 ± vo/v)f

where f ' is the frequency heard by the observer, vo is the observer's velocity,
v is the velocity of the wave, and f is the frequency of the wave.

When both the observer and the source are in motion, then the resulting
frequency which is heard by the observer can be described by:

f ' = ((v ± vo) / (v ± vs))f
where the variables are the same as before for the other equations: f ' is the resultant frequency, v is the velocity of the wave, vo is the velocity of the observer, vs is the velocity of the source, and f is the frequency of the wave.

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