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Doppler with moving source
Intermediate
Approaching sources raise pitch; receding ones lower it.
dopplerFor a source moving at v_s toward a stationary observer f' = fv/(v − v_s); wavefronts bunch up ahead and spread behind.
A 500 Hz siren at 30 m/s approaching: 548 Hz; receding: 460 Hz.
The medium speed v is unchanged.
In more detail
For a moving source and a stationary observer, the frequency is f' = f v/(v − v_s) when approaching. The wave crests are compressed in front of the source, raising the frequency.
Real-world uses
- Engineers calculate the frequency heard from approaching trains and aircraft.
- Radar guns use moving-source formulas for reflected signals.
- A train horn sounds higher as it approaches a station and lower as it passes and moves away.
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Frequently asked questions
What changes the wavelength?
The source moves forward between wave crests, shortening the wavelength ahead.
What if the source moves faster than sound?
The formula no longer applies, and a shock wave forms.
Does the speed of the source change the wave speed?
No. The sound travels at the same speed in the air; only the wavelengths it reaches the listener with are changed.
Related topics in Waves & Sound
Infrasound · Sonar and echoes · Doppler effect · Doppler with moving observer · Doppler in light · Shock waves and sonic boom