MotionLab

Doppler Effect Calculator

Why an ambulance siren sounds higher-pitched approaching and lower-pitched leaving.

Source frequency (Hz)

Source speed (m/s)

Speed of sound (m/s)

Observed frequency (Hz)

482.173

For a source approaching a stationary observer: f' = f·v / (v − vₛ)

What you entered

Source frequency (Hz): 440Source speed (m/s): 30Speed of sound (m/s): 343

1
f' = f × v ÷ (v − vₛ)
440 × 343 ÷ (343 − 30)= 482.1725 Hz

Result

Observed frequency (Hz): 482.173

A 440 Hz source approaching at 30 m/s sounds like 482.17 Hz to a stationary observer.

Doppler shift for a moving sound source

Frequency heard when a source moves toward or away from a stationary listener, with sound at 343 m/s.

Source frequency (Hz)	Source speed (m/s)	Direction	Observed frequency (Hz)
440	0	Toward	440.00
440	30	Toward	482.17
440	30	Away	404.61
1000	20	Toward	1061.92
1000	20	Away	944.90

The shifts are not symmetric: 30 m/s toward raises 440 Hz by 42.17, while the same speed away lowers it by only 35.39. That asymmetry is real and comes from the source speed sitting in the denominator, and it is why a passing siren's drop sounds larger than the approach rise felt. The change happens as the vehicle passes, not gradually. The same effect on light is redshift, which is how the expansion of the universe was discovered, though the relativistic formula differs from this classical one.

Why the pitch shifts

As a sound source approaches, each successive sound wave is emitted from a closer position, compressing the wavelength and raising the perceived frequency (pitch) — moving away does the opposite, stretching wavelength and lowering pitch.

This calculator covers the simple case

This computes the case of a moving source and stationary observer — a moving observer, a moving medium (wind), or both source and observer moving simultaneously all have their own variations of the full Doppler formula.

Frequently asked questions

An ambulance siren emits 700 Hz and approaches at 30 m/s. What frequency do I hear?

f_observed = f × v_sound/(v_sound − v_source) = 700 × 343/(343 − 30) = 700 × 1.096 = 767 Hz. As it passes and recedes: f = 700 × 343/(343 + 30) = 644 Hz. The pitch drops by about 123 Hz — a noticeable shift.

How do police radar guns use the Doppler effect?

The gun emits a microwave beam; the reflected wave has a shifted frequency proportional to the car's speed. For electromagnetic waves: Δf/f = 2v/c. A car at 100 km/h (27.8 m/s) shifts a 24 GHz beam by about 4,450 Hz — easily measurable by the receiver.

Does the Doppler effect work for light too?

Yes — astronomers use it constantly. Light from objects moving away is 'redshifted' (lower frequency), and from approaching objects is 'blueshifted.' Edwin Hubble used this to discover that distant galaxies are receding — evidence the universe is expanding.

Why does the pitch change suddenly when a car passes me?

It doesn't change suddenly — it changes continuously. But the rate of change is fastest at the moment of closest approach, creating the perception of a sudden drop. The effect is most dramatic when the source passes close and fast.