Doppler Shift Calculator
The Doppler Shift Calculator predicts the frequency a listener actually hears when a sound source, the observer, or both are moving through the air. As an ambulance siren or passing car approaches, the sound waves bunch up and the pitch rises; as it speeds away, the waves stretch out and the pitch drops. Enter the emitted frequency, the speed of sound in the medium, and the signed velocities of the observer and source, and the calculator returns the observed frequency, the frequency shift, and whether the pitch goes higher or lower.
Formula
f' = f · (v + v_o) / (v − v_s); Δf = f' − f
- f'
- Observed (heard) frequency in hertz
- f
- Source (emitted) frequency in hertz
- v
- Speed of sound in the medium (m/s)
- v_o
- Observer velocity, positive when moving toward the source (m/s)
- v_s
- Source velocity, positive when moving toward the observer (m/s)
- Δf
- Frequency shift, observed minus source (Hz)
How it works
- Enter the source frequency in hertz, the speed of sound (343 m/s in dry air at 20 degrees C by default), and the velocities of the observer and source in metres per second.
- Use the sign convention: a velocity is positive when that party moves toward the other and negative when moving away. The calculator then evaluates the Doppler formula to find the observed frequency.
- The frequency shift is the observed frequency minus the source frequency, and the pitch direction reports whether the listener hears a higher, lower, or unchanged tone.
Worked example
A car horn sounding at 1000 Hz drives toward a stationary listener at 30 m/s through air where sound travels at 343 m/s.
- Observer is still, so v_o = 0; the source approaches, so v_s = +30.
- f' = 1000 × (343 + 0) ÷ (343 − 30) = 343000 ÷ 313.
- f' = 1095.8466 Hz, giving a shift of +95.8466 Hz.
Observed frequency 1095.8466 Hz, a +95.8466 Hz shift, so the pitch is Higher.
Frequently asked questions
- How do I enter the velocities — what is the sign convention?
- Velocities are signed by direction of motion. Enter a positive value when the observer or source is moving toward the other, and a negative value when it is moving away. A positive source velocity shrinks the denominator and raises the pitch, while a positive observer velocity enlarges the numerator and also raises the pitch.
- Why does the calculator refuse a source velocity at or above the speed of sound?
- When the source reaches the speed of sound the denominator (v − v_s) becomes zero or negative, so the classical Doppler formula breaks down. Physically the source catches up with its own wavefronts and a shock wave (a sonic boom) forms, so the calculator stops rather than return a meaningless figure.
- What speed of sound should I use?
- The default 343 m/s is the speed of sound in dry air at 20 degrees C. Sound travels faster in warmer air, in water (about 1480 m/s), and in solids, so adjust the speed-of-sound field to match your medium and temperature for an accurate result.
- Does this formula apply to light or radio waves?
- No. This calculator uses the classical acoustic Doppler effect, which depends on motion relative to the medium. Light and radio waves need the relativistic Doppler formula because there is no medium and the speed of light is constant for all observers.