Why does an ambulance siren change pitch?
As it approaches, sound waves are compressed (higher frequency); as it passes and recedes, they stretch (lower frequency).
Doppler Effect Calculator (Sound)
f' = f·v/(v − vₛ)
Doppler effect calculator for a source approaching a stationary observer. Find the observed frequency shift.
Calculate
Enter values above to calculate
How it calculates
1
Source approaching a stationary observer: f' = f × v/(v − vₛ)
2
v = wave speed (343 m/s for sound in air), vₛ = source speed
3
Observed frequency is higher than emitted (blueshift)
Formula
f' = f·v/(v − vₛ)
Variable Table
| Symbol | Quantity | SI Unit |
|---|---|---|
| f' | Observed frequency | Hz |
| f | Source frequency | Hz |
| v | Wave speed | m/s |
| vₛ | Source speed (toward observer) | m/s |
→ Doppler Effect article
How to Use This Calculator
This doppler effect calculator (sound) is built for quick physics checks and worked-problem review. Enter values in the units shown beside each input, then compare the result with the formula and variable table before using it in a longer solution. The calculator does the arithmetic, but the physics still depends on choosing a model that matches the situation.
Start by identifying the system, the known quantities, and the quantity you want to find. If a value is given in a non-SI unit, convert it before substitution. A correct numerical answer with mixed units can still be physically wrong, especially when squared units, inverse seconds, charges, temperatures, or distances are involved.
Assumptions and Limits
The formula f' = f·v/(v − vₛ) is a model, not a universal description of every possible case. It assumes the quantities in the variable table are the relevant quantities for the problem and that hidden effects are either negligible or already included in the inputs. If friction, drag, relativistic speeds, changing fields, non-constant temperature, or geometry-specific effects matter, check whether a more complete model is needed.
Use the result as a magnitude and units check. Ask whether the answer has the right sign, whether it grows or shrinks when an input changes, and whether the limiting cases make sense. Setting an input to zero, doubling a quantity, or using a very large value is often enough to catch a formula choice or unit mistake before it reaches a final answer.
Worked Example
An ambulance siren (440 Hz) approaches at 30 m/s (sound = 343 m/s). Find observed pitch.
Step 1: f' = f × v/(v − vₛ)
Step 2: f' = 440 × 343/(343 − 30)
Step 3: f' = 440 × 343/313
Answer: f' ≈ 482 Hz (higher pitch)
Common Mistakes
- Approaching source raises pitch; receding lowers it
- For a moving observer (not source), the formula differs: f' = f(v ± vₒ)/v
- For light, use the relativistic Doppler formula instead
Related
Frequently Asked Questions
Does the Doppler effect work for light?
Yes, but you must use the relativistic Doppler formula. Cosmological redshift is the Doppler effect for receding galaxies.