Doppler Effect Calculator
Estimate the observed sound frequency when a source, a receiver, or both move relative to the wave-carrying medium.
Wave and motion values
Observed sound
The receiver hears a higher frequency than the source emits.
f = f₀ × (v + vᵣ) / (v + vₛ)Frequency comparison
| Quantity | Symbol | Value |
|---|---|---|
| Emitted frequency | f₀ | 700.00 Hz |
| Observed frequency | f | 726.80 Hz |
| Frequency shift | Δf | +26.80 Hz |
| Frequency ratio | f/f₀ | 1.038281 |
How to use this Doppler effect calculator
What this calculator does
This calculator estimates the frequency received from a moving sound source when the receiver, the source, or both move along the same line through a medium. It uses the classical one-dimensional Doppler relation for waves whose propagation speed is defined relative to that medium. The output is an acoustic frequency estimate, not a prediction of loudness, sound pressure level, travel time, or perceived musical pitch in a psychoacoustic sense. It also is not the relativistic formula used for light at high fractions of the speed of light. For a derivation and examples of the classical sound-wave model, see OpenStax University Physics on the Doppler effect.
When to use it
Use the calculator to check an approaching or receding siren problem, compare frequencies for a moving microphone and stationary source, explore how the speed of sound affects a shift, or verify textbook exercises where source and receiver velocities are measured relative to the air or another propagation medium. It is especially useful when both the source and receiver move, because the two velocity signs enter different parts of the equation.
How to calculate
- The calculator opens with a complete demonstration: a 700 Hz source, a 343.2 m/s wave speed, a receiver moving at – 4.166666667 m/s, and a source moving at – 16.666666667 m/s. The result and example Excel workbook are ready immediately.
- Replace the four input values with your own measurements. Values use SI units shown beside each field. A period is the accepted decimal separator; grouping separators and scientific notation are intentionally rejected to prevent ambiguous pasted values.
- Apply the sign rules carefully. Receiver velocity is positive when the receiver moves toward the source. Source velocity is positive when the source moves away from the receiver. Negative signs indicate the opposite motions.
- Read the live Observed frequency (f), then use Frequency shift (Δf), Shift percentage, and Frequency ratio (f/f₀) to judge the size and direction of the change. The Frequency comparison table repeats the same canonical results in a compact audit-friendly form.
- Choose Download Excel to export the current validated inputs and results as a real XLSX workbook. Reset clears the demonstration and all four data fields; after Reset, Excel export remains unavailable until a complete valid set is entered again.
Input guide
Emitted frequency (f₀) is a required positive decimal in hertz. A realistic example is 700 Hz for a siren tone. Raising it scales the observed frequency proportionally, while leaving the frequency ratio unchanged. Do not enter units inside the field. Wave velocity (v) is a required positive decimal in meters per second. The demonstration uses 343.2 m/s, a representative sound speed in air; the actual speed depends on the medium and conditions. Changing it alters how strongly a given source or receiver speed affects the result. A common mistake is mixing km/h with m/s.
Receiver velocity (vᵣ) is a required signed decimal in m/s. The demonstration value – 4.166666667 m/s corresponds to 15 km/h moving away from the source. Positive values mean motion toward the source, which increases the numerator and tends to raise the observed frequency. Source velocity (vₛ) is a required signed decimal in m/s. The demonstration value – 16.666666667 m/s corresponds to 60 km/h moving toward the receiver. Because it appears in the denominator, a negative source velocity tends to raise the observed frequency. The source denominator must remain greater than zero, and the receiver term must not imply a negative received frequency.
Output guide
Observed frequency (f) is the calculated received frequency in hertz and is the primary result. Frequency shift (Δf) is observed minus emitted frequency, so zero means no net frequency change, positive means an upward shift, and negative means a downward shift. Shift percentage divides the frequency shift by emitted frequency and expresses the change as a percent. Frequency ratio (f/f₀) is a dimensionless comparison: 1 means unchanged, above 1 means higher, and below 1 means lower. The header pills labeled Emitted, Observed, and Shift provide the same current-state summary at a glance.
The Frequency comparison table has three columns. Quantity identifies the metric, Symbol gives its standard notation, and Value reports the current formatted result. These values are exact consequences of the entered model apart from display rounding; the workbook stores the underlying numeric values rather than scraping the rounded page text.
Worked example
With f₀ = 700 Hz, v = 343.2 m/s, vᵣ = – 4.166666667 m/s, and vₛ = – 16.666666667 m/s, the formula gives 700 × (343.2 – 4.166666667) ÷ (343.2 – 16.666666667) = approximately 726.796652 Hz. The calculator displays 726.80 Hz. The corresponding shift is +26.80 Hz, the shift percentage is +3.83%, and the frequency ratio is 1.038281. Rounded to the nearest whole hertz, the received tone is about 727 Hz.
Learn more
The Doppler effect is used far beyond roadside-siren examples. The U.S. National Weather Service explains how Doppler radar uses phase shifts to infer radial motion, while MedlinePlus describes how Doppler ultrasound uses reflected sound to examine blood flow. Those systems add instrument-specific geometry and signal processing; this calculator stays with the simpler direct one-dimensional classical relation.
Understanding the sign convention and limits
The model is easiest to use if you treat the propagation medium as the reference frame. The receiver term appears as v + vᵣ, so moving toward the source makes vᵣ positive and increases the rate at which wavefronts meet the receiver. The source term appears as v + vₛ, so moving away makes vₛ positive and stretches the spacing of emitted wavefronts. A source approaching the receiver therefore has a negative vₛ, reducing the denominator and raising the observed frequency.
Do not substitute a single relative speed for the two velocities unless the specific setup justifies it. For sound, motion relative to the medium matters, which is why wind and different propagation conditions can complicate real measurements. Also avoid the singular source condition v + vₛ = 0: the simple formula ceases to provide a finite result there. Cases involving shock waves, supersonic source motion toward the receiver, reflected-wave double shifts, or relativistic electromagnetic waves require a model tailored to those conditions.
Interpreting sensitivity
For fixed wave speed and emitted frequency, moving the receiver more strongly toward the source raises the result almost linearly because receiver velocity is in the numerator. Moving the source more strongly toward the receiver can have a sharper effect because source velocity changes the denominator. When both velocities are small compared with wave speed, shifts are modest. As the denominator approaches zero from the positive side, the classical expression grows rapidly, signaling that the simple continuous-wave model is reaching a physical boundary rather than promising an arbitrarily large real-world frequency.