Doppler Effect
Observed frequency shift due to relative motion.
Formula
Variables
Example
An ambulance siren rises in pitch as it approaches, then drops as it passes — the Doppler effect.
How it works
The Doppler effect gives the frequency an observer measures when a wave source and observer move relative to each other. If the observer moves toward incoming wavefronts, they meet more wave crests per second so the observed frequency increases; if the source moves toward the observer, it compresses the wavefronts in front of it so the wavelength decreases and the frequency rises. The signs in the formula encode these two geometric effects: motion toward each other raises the observed frequency, while motion away lowers it.
When to use it
Use this for sound problems involving moving sirens, trains, bats, or medical ultrasound, and for any wave-based situation where either the source or the observer is moving along the line of travel. It is also the standard starting point for radar-like wave measurements and astronomical redshift/blueshift calculations in the nonrelativistic limit.
Worked example, step by step
A train whistle emits a tone of f = 600 Hz. The speed of sound is v = 340 m/s. An observer stands still while the train moves toward them at v_s = 25 m/s. Because the observer is stationary, v_o = 0. For a moving source approaching the observer, use f' = f(v + v_o)/(v - v_s). Substitute the values: f' = 600(340 + 0)/(340 - 25) Compute the denominator: 340 - 25 = 315 So f' = 600 × 340 / 315 f' = 204000 / 315 f' ≈ 647.6 Hz Final answer: the observer hears about 648 Hz.
Common mistakes to avoid
- Using the same sign for both source and observer motion instead of treating approach and recession separately
- Forgetting that the wave speed v is the speed in the medium, not the speed of the source
- Mixing up source speed and observer speed, especially when both are moving
Did You Know?
The Doppler effect — the drop in a passing siren's pitch — also lets astronomers measure the universe's expansion.
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