Doppler Frequency Shift
Δf = fc × v / c
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Formula
Description
The Doppler effect shifts the frequency of electromagnetic waves when there is relative motion between transmitter and receiver. The frequency increases when approaching (positive shift) and decreases when receding (negative shift). This simplified formula is valid for velocities much less than the speed of light (v << c), which covers all terrestrial applications. Doppler shift is the fundamental principle behind police radar guns, weather radar, automotive radar (ACC, collision avoidance), medical ultrasound velocity measurement, and satellite communication frequency planning.
Variables
- Δf — Doppler frequency shift (Hz)
- f_c — Carrier (transmitted) frequency (Hz)
- v — Relative velocity between source and observer (m/s)
Practical Notes
c = 299,792,458 m/s. At 24 GHz (automotive radar), a car at 100 km/h (27.8 m/s) produces Δf = 24e9 × 27.8/3e8 = 2222 Hz. At 77 GHz: Δf = 7122 Hz. For radar, the round-trip doubles the Doppler shift: Δf_radar = 2 × fc × v/c. GPS satellite Doppler shifts are ±5 kHz due to satellite orbital velocity of ±800 m/s relative to the receiver.
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