Calculator Inputs
Use the air model for sound in normal air. Use custom medium speed for water, solids, or any known wave speed.
Formula used
Classical sound Doppler equation
fo = fs × (v + σovo) / (v - σsvs)
Here, σ = +1 for motion toward and σ = -1 for motion away.
Observed frequency
fo = fs(v + σovo)/(v - σsvs)
Source speed
vs = [v - (fs/fo)(v + σovo)] / σs
Listener speed
vo = [(fo/fs)(v - σsvs) - v] / σo
- fs = source frequency
- fo = observed frequency
- v = wave speed in the medium
- vs = source speed magnitude
- vo = listener speed magnitude
This page applies the classical Doppler model for waves in a medium, especially sound. It is not the relativistic light-frequency equation.
How to use this calculator
- Choose the calculation mode for observed frequency, source speed, or listener speed.
- Select how to define the medium speed: air temperature or a custom known wave speed.
- Enter the source frequency and fill the known motion values.
- Set whether the source and listener move toward or away.
- Pick a speed unit for inputs and outputs.
- Press Calculate Doppler Shift to show the result block above the form.
- Review the chart, summary table, and interpretation.
- Use the export buttons to save the result as CSV or PDF.
Example data table
| Case | Source frequency (Hz) | Medium speed (m/s) | Source speed (m/s) | Listener speed (m/s) | Directions | Observed frequency (Hz) | Wavelength (m) |
|---|---|---|---|---|---|---|---|
| Ambulance approaches a stationary listener | 700 | 343 | 20 | 0 | Source toward, listener toward | 743.34 | 0.461429 |
| Source moves away from a stationary listener | 600 | 343 | 15 | 0 | Source away, listener toward | 574.86 | 0.596667 |
| Listener moves toward a stationary source | 500 | 343 | 0 | 12 | Source toward, listener toward | 517.49 | 0.686000 |
| Both source and listener move toward each other | 800 | 343 | 18 | 10 | Source toward, listener toward | 868.92 | 0.406250 |
FAQs
1. What does this Doppler calculator solve?
It solves the classical Doppler effect for sound or any wave in a medium. You can calculate observed frequency, source speed, or listener speed using direction-aware motion inputs.
2. When should I use the air temperature option?
Use the air model when you want the sound speed estimated from air temperature. It is helpful for classroom physics, outdoor siren problems, and approximate real-world sound calculations.
3. What does “toward” or “away” change?
Direction changes the sign inside the Doppler equation. Motion toward increases arrival rate, while motion away decreases it. Picking the wrong direction can make inverse speed results physically inconsistent.
4. Is this valid for light and astronomy?
Not for relativistic light. This page uses the classical wave-in-medium model, which fits sound best. For light, use the relativistic Doppler equation instead.
5. Why does the calculator show wavelength too?
A moving source changes the wavefront spacing in the medium. Showing wavelength helps you connect frequency change with compressed or stretched wavefronts and understand the physical picture.
6. Can the source speed equal the medium speed?
For an approaching source, the denominator can collapse as source speed nears medium speed. That creates a singular case, so the calculator blocks invalid combinations that break the classical equation.
7. What does the chart represent?
The chart plots observed frequency against the currently active speed variable. It helps you see sensitivity, nonlinearity, and how quickly the frequency changes as motion increases.
8. What do the CSV and PDF downloads include?
They export the current result summary. CSV is useful for spreadsheets and bulk records, while PDF is convenient for reports, homework attachments, and quick sharing.