Doppler Effect Calculator
Calculate the apparent frequency shift of a wave caused by relative motion between source and observer.
Wave Parameters
Apparent Frequency Result
Calculate the apparent frequency shift above.
Doppler Effect Calculator: Analyzing Wave Frequency Shifts
Welcome to the Doppler Effect Calculator, a specialized wave physics tool used to measure the apparent change in frequency or wavelength experienced by an observer moving relative to the source of the wave. While most commonly experienced daily as the sudden shift in pitch of a passing ambulance siren, this principle fundamentally governs radar, astronomy (redshift), and medical sonography. Use our calculator to determine exactly what pitch you will hear, whether the source and receiver are barreling towards each other or moving away at high velocities.
Formulas Behind The Doppler Shift
The General Doppler Equation
f' = f₀ * [(v ± v_observer) / (v ∓ v_source)]
Where f' is the apparent observer frequency, f₀ is the original emitted frequency, and v is the speed of the wave in the medium (e.g. sound in air at 343 m/s).
- Use the top signs (+ in numerator, - in denominator) when the source and observer are moving towards each other (pitch increases).
- Use the bottom signs (- in numerator, + in denominator) when the source and observer are moving away from each other (pitch decreases).
How to Calculate Apparent Shift
- State Wave Properties: Input the unadulterated frequency of the source (in Hertz) and the propagation velocity of the wave. By default, the speed of sound in air is approximately 343 m/s.
- Specify Source Motion: Determine how fast the source object is moving (in m/s), and select whether it is driving towards or steering away from the destination observer.
- Specify Observer Motion: Determine how fast the observer is moving, and select if they are heading towards the source or retreating away in the opposite direction. (Set to 0 if standing completely still).
- Evaluate Pitch: Press the Calculate button! The algebraic engine handles all sign-flipping numerator mechanics to output the exact heard frequency safely.
Example Calculation: Passing Ambulance
Scenario: Hearing the Siren Approach
An ambulance driving at 30 m/s is heading towards a stationary pedestrian. The ambulance has its siren emitting at exactly 700 Hz. The speed of sound is 343 m/s. What pitch does the pedestrian hear?
Known Constants: f₀ = 700 Hz, v = 343 m/s, v_source = 30 m/s (Towards), v_observer = 0 m/s
Computation:
- The engine applies the "Towards" rule: the source denominator decreases (v - v_source).
- f' = 700 * [(343 + 0) / (343 - 30)]
- f' = 700 * (343 / 313)
- f' ≈ 700 * 1.0958 ≈ 767.1 Hz.
Result: Before the ambulance passes, the pedestrian hears a noticeably higher-pitched 767.1 Hz siren! Once it passes, the denominator flips to (343 + 30), plummeting the apparent pitch drastically.
Academic & Scientific References
For further understanding and validation of the formulas used above, we recommend exploring these authoritative resources: