Doppler Effect Calculator
Observed Freq (Approaching)
—
Observed Freq (Receding)
—
Frequency Shift (Approaching)
—
Frequency Shift (Receding)
—
How the Doppler Effect Works
The Doppler effect is the change in observed frequency of a wave caused by relative motion between the wave source and the observer. When the source approaches, wavefronts compress and the observer perceives a higher frequency; when the source recedes, wavefronts stretch and the frequency drops. First proposed by Austrian physicist Christian Doppler in 1842 and experimentally confirmed by Buys Ballot in 1845, this principle underlies a remarkable range of technologies from police radar to medical imaging.
The effect applies to all wave types: sound waves in air, electromagnetic waves (light, radio, microwaves), and even water waves. For sound, the Doppler shift depends on the medium's wave speed (approximately 343 m/s in air at 20 degrees C). For light, the shift follows relativistic equations since photons travel at the speed of light regardless of the reference frame. Use our Acceleration Calculator to determine object velocities before plugging them into this Doppler calculator.
The Doppler Effect Formula
The classical Doppler formula for sound waves, as defined in standard physics references such as OpenStax University Physics, is:
f' = f x (c + vo) / (c - vs) (approaching)
f' = f x (c - vo) / (c + vs) (receding)
Where:
- f' = observed frequency (Hz)
- f = source frequency (Hz)
- c = speed of sound in the medium (m/s)
- vo = observer velocity toward (+) or away from (-) the source
- vs = source velocity toward (+) or away from (-) the observer
Worked example: An ambulance siren emits at 700 Hz and travels toward a stationary observer at 30 m/s. f' = 700 x (343 + 0) / (343 - 30) = 700 x 343/313 = 767.1 Hz. As it passes and moves away: f' = 700 x (343 - 0) / (343 + 30) = 700 x 343/373 = 643.7 Hz. The total pitch drop is 123.4 Hz, clearly audible.
Key Terms You Should Know
- Frequency (Hz): The number of wave cycles per second. Human hearing ranges from about 20 Hz to 20,000 Hz. Middle C on a piano is 261.6 Hz; concert A is 440 Hz.
- Mach number: The ratio of an object's speed to the speed of sound. Mach 1 equals the speed of sound (343 m/s at 20 degrees C). Mach 2 is twice the speed of sound.
- Redshift: The decrease in observed frequency (increase in wavelength) when a light source moves away from the observer. Used in astronomy to measure recession velocities of galaxies.
- Blueshift: The increase in observed frequency when a light source moves toward the observer. The Andromeda Galaxy exhibits blueshift because it is approaching the Milky Way.
- Sonic boom (shock wave): The intense sound wave created when a source exceeds Mach 1. The classical Doppler formula produces a division by zero at vs = c.
Speed of Sound in Different Media
The Doppler shift depends on the wave propagation speed. Sound travels at different speeds through different media, which changes the magnitude of frequency shifts for the same relative velocities.
| Medium | Speed (m/s) | Speed (mph) | Notes |
|---|---|---|---|
| Air (0 degrees C) | 331 | 741 | Increases ~0.6 m/s per degree C |
| Air (20 degrees C) | 343 | 767 | Standard reference condition |
| Water (25 degrees C) | 1,497 | 3,349 | Used in sonar and marine Doppler |
| Steel | 5,960 | 13,332 | Used in non-destructive testing |
| Light (vacuum) | 299,792,458 | 670,616,629 | Relativistic Doppler formula applies |
Practical Doppler Effect Examples
Example 1: Police radar gun. A radar gun emits microwaves at 24.15 GHz. A car approaching at 100 km/h (27.8 m/s) causes a Doppler shift of approximately 4,410 Hz. The gun measures this shift to calculate vehicle speed with accuracy within 1 mph. Over 100 million traffic citations per year in the U.S. rely on Doppler radar technology.
Example 2: Medical ultrasound. Doppler ultrasound measures blood flow velocity by bouncing sound waves (typically 2-10 MHz) off moving red blood cells. Normal blood flow in the carotid artery is about 60-100 cm/s. A significant reduction suggests stenosis. The FDA-cleared diagnostic Doppler devices are used in millions of cardiovascular exams annually.
Example 3: Astronomical redshift. The galaxy NGC 4889 has a redshift z = 0.0215, meaning its light is shifted 2.15% toward longer wavelengths. Using the Doppler relation v = z x c, its recession velocity is about 6,450 km/s. Use our Force Calculator and Pendulum Calculator for related physics problems.
Tips for Using This Calculator
- Use consistent units. All speeds must be in the same unit (m/s). Convert km/h to m/s by dividing by 3.6; convert mph by dividing by 2.237.
- Source speed must be less than the speed of sound. If vs equals or exceeds c, the formula produces undefined or negative results because the source has exceeded the sonic barrier.
- For stationary sources, set source speed to 0. This simplifies the formula to f' = f x (c + vo) / c, useful for scenarios where only the observer moves (e.g., driving past a stationary siren).
- Temperature matters for precision. The speed of sound in air varies by about 0.6 m/s per degree Celsius. Use 331 + (0.606 x T) for accurate results at non-standard temperatures.
- This calculator uses the classical formula. For objects moving at significant fractions of the speed of light, the relativistic Doppler formula must be used instead. The classical formula is accurate for everyday sound and low-speed applications.
Frequently Asked Questions
What is the Doppler effect?
The Doppler effect is the change in observed frequency of a wave caused by relative motion between the source and observer. When they approach, the observed frequency increases (higher pitch for sound, blueshift for light). When they recede, the observed frequency decreases (lower pitch, redshift). Named after Christian Doppler who proposed it in 1842, the effect applies to all wave types. The classic everyday example is the changing pitch of an ambulance siren as it passes by.
What is the Doppler effect formula for sound waves?
The Doppler formula for sound is f' = f x (c + v_o) / (c - v_s) when approaching, where f is the source frequency, c is the speed of sound (343 m/s at 20 degrees C), v_o is the observer speed, and v_s is the source speed. For receding motion, the signs flip. For example, a 440 Hz source approaching at 30 m/s gives f' = 440 x 343/313 = 482.1 Hz, an increase of about 42 Hz.
Does the Doppler effect apply to light?
Yes, the Doppler effect applies to electromagnetic radiation including visible light. Stars and galaxies moving away appear redshifted, while those approaching appear blueshifted. Edwin Hubble used this principle in 1929 to demonstrate that distant galaxies are receding, providing key evidence that the universe is expanding. The relativistic Doppler formula for light differs from the classical sound formula because light does not require a medium.
How is the Doppler effect used in everyday technology?
The Doppler effect has numerous practical applications. Police radar guns measure vehicle speed by bouncing microwaves off cars and measuring the frequency shift. Medical Doppler ultrasound measures blood flow velocity to detect blockages. Weather Doppler radar detects precipitation movement and wind patterns. Satellite navigation systems apply Doppler corrections for accuracy. Even automatic door sensors use the Doppler effect to detect approaching people.
What is a sonic boom and how does it relate to the Doppler effect?
A sonic boom occurs when a sound source exceeds the speed of sound (Mach 1, approximately 343 m/s or 767 mph at sea level). At this point, the Doppler formula produces a division by zero because v_s equals c. Physically, the sound waves pile up into a concentrated shock wave called a Mach cone. The half-angle equals arcsin(c/v_s). Military jets regularly exceed Mach 1, and the Concorde cruised at Mach 2.04, producing a sonic boom audible on the ground.
How does temperature affect the Doppler effect for sound?
Temperature directly affects the speed of sound, which changes the magnitude of the Doppler shift. The speed of sound in air is approximately 331.3 + (0.606 x temperature in Celsius) m/s. At 0 degrees C, sound travels at 331 m/s; at 20 degrees C, it is 343 m/s; at 40 degrees C, it reaches 355 m/s. A higher speed of sound reduces the proportional frequency shift for the same velocities. This matters for precision applications like acoustic measurements.