Calculator Inputs
Formula Used
For sound in a stationary medium, the Doppler relation is:
f′ = f · ( v + vo ) / ( v − vs )
Here v is sound speed, vo is observer speed, and vs is source speed.
This calculator applies a sign convention: speeds are positive when moving toward the other party, and negative when moving away. Choose “Approaching” or “Receding” to set those signs.
Note: For very high speeds or for light, different relativistic equations are required.
How to Use
- Choose what you want to solve for (speed or frequency).
- Select motion direction: approaching increases pitch, receding lowers it.
- Pick a medium preset or enter a custom sound speed.
- Enter the known frequency values and any known speeds.
- Press Calculate to see results above the form, then export if needed.
Example Data Table
| Case | f (Hz) | f′ (Hz) | v (m/s) | vo (m/s) | Solved vs (m/s) |
|---|---|---|---|---|---|
| Approaching | 1000 | 1100 | 343 | 0 | 31.18 |
| Approaching | 750 | 800 | 343 | 5 | 24.61 |
| Receding | 1200 | 1100 | 343 | 0 | 28.09 |
Examples assume the stationary-medium sound model and the sign rule stated above.
Doppler Effect Speed Guide
1) What the calculator estimates
This tool estimates motion using a measured frequency shift. For sound, the observed pitch rises when the source and observer move closer, and it falls when they separate. The core output is a solved target plus the ratio f′/f, the shift in hertz, and percent change.
2) Typical sound speeds by medium
Sound speed depends on the medium and temperature. Dry air near 20 °C is about 343 m/s, while freshwater is about 1482 m/s. A simple air model is v ≈ 331.3 + 0.606·T(°C). Changing v directly affects the computed speed.
3) Useful frequency ranges
Audible sound is roughly 20–20,000 Hz. Many sirens sit near 400–1500 Hz, and musical notes are often 100–2000 Hz. Larger base frequencies make small speed differences easier to detect because the absolute shift (Hz) becomes more noticeable.
4) Approaching vs. receding data
Approaching cases commonly show f′ > f, so the ratio f′/f exceeds 1. Receding cases usually show f′ < f, so the ratio is below 1. In field measurements, repeat several passes and average the ratio to reduce noise.
5) Source speed and observer speed
The calculator lets you solve for source speed, observer speed, sound speed, or either frequency. For example, with a stationary observer (vo=0), solving for vs uses the ratio r = f′/f to estimate how fast the source must move to create that shift.
6) Practical measurement tips
Use a stable tone, record at a high sample rate, and estimate frequency with an FFT or tuner app. Keep the microphone aligned with motion to reduce angle effects. Avoid strong echoes; reflections can create mixed peaks and inflate the detected shift.
7) Interpreting the results
The signed speeds shown are positive for “toward” and negative for “away,” based on your direction choice. The magnitude conversions to km/h and mph help compare with real motion. If the source speed approaches the sound speed, the simple model becomes unreliable.
8) Where this model should not be used
This page targets sound in a stationary medium. For electromagnetic waves, use the relativistic Doppler formula instead. Also, if wind is strong, or the medium itself moves, the effective sound speed relative to the observer changes and you should model that flow explicitly.
FAQs
1) Why does pitch increase when something approaches?
As distance closes, wavefronts reach you more frequently. The effective period shortens, so measured frequency increases. The calculator expresses this as a ratio f′/f greater than 1 for approaching motion.
2) What sound speed should I use for air?
A common default is 343 m/s around 20 °C. If temperature differs, the tool’s temperature-based option uses v ≈ 331.3 + 0.606·T(°C) to improve accuracy.
3) Can I solve for observer speed instead of source speed?
Yes. Choose “Observer speed” in the Solve for menu. Enter the emitted and observed frequencies, sound speed, and any known source speed, then the tool computes the observer speed consistent with the shift.
4) What units are supported for speeds?
You can enter speeds in m/s, km/h, or mph. Internally the calculator converts values to m/s for computation, then provides helpful magnitude conversions back to km/h and mph in the results.
5) What does a negative solved speed mean?
It follows the selected sign convention. With “Receding,” speeds are treated as negative (away). The magnitude still indicates how fast the motion is; the sign indicates whether it is toward or away.
6) My ratio is close to 1. Is the result reliable?
When f′/f is near 1, the shift is small and measurement noise matters more. Record longer samples, average multiple runs, and ensure a stable tone to reduce uncertainty.
7) Why does the tool warn about source speed near sound speed?
The simple stationary-medium sound model assumes vs is well below v. As vs approaches v, the denominator (v − vs) shrinks, results become sensitive, and shock effects may appear.