An ambulance siren sounds higher as it approaches and lower as it leaves. The waves bunch up in front of a moving source and stretch out behind it. The same effect is used by radar guns, weather radar and astronomers measuring star motion.
How to use the Doppler Effect Calculator
- Emitted frequency f₀
- Medium (wave velocity)
- Custom wave velocity
- Velocity of the receiver v_r
- Velocity of the source v_s
Results update as you type, every field has its own unit menu, and everything is calculated in your browser.
How it works
Enter the emitted frequency, the wave speed in the medium and the two velocities. Use negative velocities for motion away from the other party.
Inputs explained
| Field | What to enter |
|---|---|
| Emitted frequency f₀ | Units: Hz, kHz, MHz, GHz, THz, rpm |
| Medium (wave velocity) | Choose one: Air at 0 °C, Air at 20 °C, Air at 40 °C, Helium at 20 °C … |
| Custom wave velocity | Units: m/s, km/h, mph, ft/s, knots |
| Velocity of the receiver v_r | Units: m/s, km/h, mph, ft/s, knots |
| Velocity of the source v_s | Units: m/s, km/h, mph, ft/s |
What each result means
- Observed frequency f = [Emitted frequency f₀]×([v] + [Velocity of the receiver v_r])÷([v] – [Velocity of the source v_s])
- Frequency shift = [Emitted frequency f₀]×([v] + [Velocity of the receiver v_r])÷([v] – [Velocity of the source v_s]) – [Emitted frequency f₀]
- Shift in percent = (([v] + [Velocity of the receiver v_r])÷([v] – [Velocity of the source v_s]) – 1)×100
Example values
How the main result changes when Emitted frequency f₀ changes and everything else stays at the example values above:
| Emitted frequency f₀ (Hz) | Observed frequency f (Hz) |
|---|---|
| 350 | 377.4984 |
| 525 | 566.2476 |
| 700 | 754.9969 |
| 875 | 943.7461 |
| 1,050 | 1,132.4953 |
| 1,400 | 1,509.9937 |
Formula
f = f₀ · (v + v_r) / (v − v_s)
v_r > 0 if the receiver moves towards the source; v_s > 0 if the source moves towards the receiver
Worked example
Inputs: Emitted frequency f₀: 700 Hz; Medium (wave velocity): Air at 20 °C; Velocity of the receiver v_r: 0 m/s; Velocity of the source v_s: 25 m/s.
Results: Observed frequency f = 754.99686 Hz; Frequency shift = 54.99686 Hz; Shift in percent = 7.857 %.
Key terms
- Doppler shift
- Change of observed frequency due to relative motion.
Frequently asked questions
Why does a siren change pitch?
Its waves are compressed ahead and stretched behind as it moves.
What happens if the source moves at the speed of sound?
The waves pile up into a shock wave, a sonic boom.
Does the Doppler effect work for light?
Yes, it causes red- and blueshifts, but uses a relativistic formula.
Which sign should I use?
Positive for motion towards the other party, negative for away.