Doppler Shift Calculator
Calculate the observed frequency based on source and observer velocities.
Wave Properties
Speed of Sound ≈ 343 m/s
Source Movement
Moving Towards Observer
Moving Away from Observer
Observer Movement
Moving Towards Source
Moving Away from Source
Observed Frequency:
0 Hz
Frequency Shift:
0 Hz
Source Wavelength:
0 m
Observed Wavelength:
0 m
Understanding the Doppler Effect
The Doppler Effect is the change in frequency or wavelength of a wave in relation to an observer who is moving relative to the wave source. It is commonly observed in sound waves, such as the changing pitch of a siren as an ambulance passes by, but it also applies to light and other electromagnetic waves.
How to Use This Calculator
To calculate the observed frequency shift, follow these steps:
- Wave Velocity: Enter the speed of the wave in the medium. For sound in air at 20°C, this is approximately 343 m/s.
- Source Frequency: Enter the original frequency emitted by the source in Hertz (Hz).
- Source Speed & Direction: Input how fast the source (e.g., a car) is moving and whether it is approaching or receding from the observer.
- Observer Speed & Direction: Input how fast the observer is moving and their direction relative to the source.
The Doppler Shift Formula
This calculator uses the general Doppler formula for sound waves:
f_obs = f_s * ( (v ± v_obs) / (v ∓ v_s) )
Where:
- f_obs = Observed Frequency
- f_s = Source Frequency
- v = Speed of the wave (e.g., speed of sound)
- v_obs = Speed of the observer
- v_s = Speed of the source
The signs (plus or minus) are determined by the direction of travel:
- Observer: Add speed if moving towards source, subtract if moving away.
- Source: Subtract speed if moving towards observer (compressing waves), add speed if moving away (stretching waves).
Example Calculation
Imagine an ambulance emitting a siren at 700 Hz approaches a stationary observer at 30 m/s. The speed of sound is 343 m/s.
Using the formula: f_obs = 700 * (343 / (343 - 30))
The observed frequency would be approximately 767 Hz, resulting in a higher pitch.