Doppler Effect Calculator

What is the Doppler effect?

When a source of sound and a listener move relative to each other, the frequency heard differs from the frequency emitted. The siren of an approaching ambulance sounds higher, and lower as it moves away. This is the Doppler effect.

Formula

f' = f × (v ± vo) / (v ∓ vs)

Here f is the source frequency, v the speed of sound in the medium, vo the speed of the observer and vs the speed of the source. The sign rule:

• Observer moving toward the source: plus on top. Moving away: minus
• Source moving toward the observer: minus below. Moving away: plus

In short, approach raises the frequency and recession lowers it. In the calculator you enter speeds as positive numbers and pick the direction from a list.

Example

An ambulance with a 1000 Hz siren approaches a stationary person at 30 m/s (108 km/h), with the speed of sound at 340 m/s. The frequency heard is 1000 × 340 / (340 − 30) = 1097 Hz. After it passes and moves away, 1000 × 340 / (340 + 30) = 919 Hz is heard. The pitch drops by 178 Hz as it goes by.

Is it the source or the observer that moves?

The two do not give the same result. A moving source squeezes the waves ahead of it and shortens the wavelength. A moving observer leaves the wavelength unchanged and simply meets the waves more often. A source approaching at 30 m/s gives 1097 Hz, while an observer approaching at the same speed hears 1088 Hz.

Limits

The formula is for sound in still air. Source and observer must move along the same line. If the source reaches the speed of sound the formula breaks down. Light, radar and radio waves follow the relativistic relation.