Doppler Effect Calculator

How it works

1. 1Enter the source frequency (Hz), wave speed (m/s), observer velocity, and source velocity.
2. 2The calculator applies f′ = f·(v + v_observer) ÷ (v − v_source) using the standard Doppler formula.
3. 3The observed frequency, frequency shift, and pitch direction (rising or falling) are shown instantly.

Use cases

• Predict the pitch change of an ambulance or police siren as it drives past.
• Analyse radar and sonar return frequencies for speed detection.
• Understand the redshift and blueshift of light from moving astronomical objects.

Frequently asked questions

What is the Doppler effect formula?

The observed frequency is f′ = f·(v + v_observer) ÷ (v − v_source), where f is the source frequency, v is the wave speed in the medium, v_observer is the observer’s velocity, and v_source is the source’s velocity. If the denominator reaches zero (the source moves at the wave speed) the result is undefined.

What is the sign convention for velocities?

Observer velocity is positive when moving toward the source; source velocity is positive when moving toward the observer. Moving apart uses negative values. A stationary observer (0 m/s) with a source approaching at 30 m/s both use positive numbers because the source is closing the gap.

Worked example — a 1000 Hz siren approaching at 30 m/s in air?

With f = 1000 Hz, v = 343 m/s, observer 0 m/s, source 30 m/s: f′ = 1000·(343 + 0) ÷ (343 − 30) = 343,000 ÷ 313 ≈ 1096 Hz — the pitch rises ~96 Hz. Once it passes (source −30 m/s): f′ ≈ 920 Hz, a drop of ~80 Hz.