The Doppler Effect

A police siren shifts from high-pitched to low as the car races past. A star moving away from Earth looks slightly redder than it should. Both are the same phenomenon: the Doppler effect — how motion changes the perceived frequency of a wave.

What Is the Doppler Effect?

Waves — whether sound or light — spread outward from a source at a fixed speed. If the source is stationary, the wave crests arrive at equal intervals: a steady frequency.

If the source is moving toward you, each new wave crest is emitted from a position slightly closer than the last — the crests bunch together and arrive more frequently. You perceive a higher pitch (for sound) or a shorter wavelength (for light).

If the source is moving away from you, the crests spread apart — lower pitch or longer wavelength.

Key insight: The speed of the wave through the medium does not change. Only the spacing of the crests changes, which changes the frequency you observe.

Sound: The Ambulance Example

Stand on a pavement as an ambulance approaches. The siren emits sound at, say, 700 Hz. Because the ambulance is moving toward you at 30 m/s, the sound crests in front of the vehicle are compressed — you hear something closer to 770 Hz, a noticeably higher pitch.

The moment the ambulance passes, you are now behind it. The crests are stretched out — the pitch drops to around 640 Hz. The drop happens almost instantly as the source crosses your position.

Note: The ambulance's own siren never changes. The driver hears 700 Hz the whole time. The shift is only perceived by observers who are moving relative to the source.

The Formula

For sound in a medium at rest, the observed frequency f' is:

f' = f · (v + v_o) / (v − v_s)

f — emitted frequency (Hz)
v — speed of sound in air (~343 m/s at 20 °C)
v_o — speed of the observer (positive if moving toward source)
v_s — speed of the source (positive if moving toward observer)

For the ambulance example (source moving toward observer at 30 m/s, observer stationary):

f' = 700 · (343 + 0) / (343 − 30) = 700 · 343/313 ≈ 767 Hz

After the ambulance passes (source moving away):

f' = 700 · 343 / (343 + 30) ≈ 644 Hz

Rule of thumb: Every 1% of the speed of sound an object moves toward you increases the perceived frequency by about 1%.

Everyday Applications

Radar and Speed Cameras

Traffic radar guns emit a microwave pulse at a known frequency. The pulse reflects off a moving car and returns Doppler-shifted. By measuring the shift, the gun calculates the car's speed to within ±1 km/h.

Medical Ultrasound

Doppler ultrasound measures blood flow. A transducer sends an ultrasound pulse into tissue; red blood cells reflecting the pulse are moving, so the echo returns at a shifted frequency. The shift reveals blood velocity and direction — essential for detecting heart valve problems or DVT.

Bat Echolocation

Bats emit ultrasonic chirps and listen for Doppler-shifted echoes from flying insects. Some species can detect velocity differences of less than 1 cm/s, enabling them to track fast-moving prey in complete darkness.

Weather Radar

NEXRAD Doppler weather radar measures the frequency shift of radio waves reflected by rain droplets. Colour maps showing wind speed and direction — including tornado rotation — are produced entirely from these Doppler measurements.

The Doppler Effect for Light

Light has no medium: it travels at c = 3 × 10⁸ m/s in vacuum regardless of the motion of source or observer. The Doppler formula must therefore use special relativity:

f' = f · √( (1 + β) / (1 − β) )

where β = v/c. For speeds much less than c, this reduces to the classical formula. At everyday speeds the relativistic correction is negligible; for stars moving at thousands of km/s it is measurable.

Source approaching → shorter wavelength → blueshift
Source receding → longer wavelength → redshift

Redshift and the Expanding Universe

In 1929, Edwin Hubble measured the spectra of distant galaxies and found that nearly all of them were redshifted: their spectral lines were shifted to longer wavelengths. The more distant the galaxy, the greater the redshift.

Hubble's conclusion: the universe is expanding. Distant galaxies are not moving through space but being carried apart as space itself stretches. The redshift is therefore a "cosmological" redshift — a cousin of the Doppler effect, but caused by the expansion of space rather than simple relative motion.

Cosmic Microwave Background: The oldest light in the universe — emitted 380 000 years after the Big Bang as X-rays — has been cosmologically redshifted by a factor of ~1100. We observe it today as microwave radiation at 2.7 K.

Measuring the Universe's Expansion Rate

The Hubble constant H₀ ≈ 70 km/s per Megaparsec quantifies how fast the universe expands. A galaxy 1 Megaparsec (3.26 million light-years) away recedes at ~70 km/s; at 10 Mpc it recedes at ~700 km/s. This was derived entirely from Doppler redshift measurements.

Try It Yourself

Explore the Doppler effect visually in the wave simulation — you can adjust the source velocity and watch how wave fronts compress ahead of the source and expand behind it.

🌊 Open Wave Simulation →

For the stellar redshift, explore the galaxy simulation to see spiral arms and the relative motions of stars:

🌌 Open Galaxy Simulation →