〰 Doppler Effect
Simulation of a moving wave source and a frequency-shift calculator for source and observer speeds.
Source speed w0.40
Emission frequency3.75 Hz
Source motion:
Quick:
What the observer sees (relative to the emitted λ₀ and f₀)
0.40
Mach number
0.60 λ₀
Wavelength in front
1.40 λ₀
Wavelength behind
1.67 f₀
Frequency in front
0.71 f₀
Frequency behind
Subsonic
Motion regime
In front: λ = (1 − v/c)·λ₀, f = f₀ / (1 − v/c)
Behind: λ = (1 + v/c)·λ₀, f = f₀ / (1 + v/c)
Mach cone (v > c): sin α = c / v
Behind: λ = (1 + v/c)·λ₀, f = f₀ / (1 + v/c)
Mach cone (v > c): sin α = c / v
- “Like the original” mode: the source oscillates sinusoidally around the center, x = W/2 + 0.35·W·sin(3w·t). The speed varies from zero at the turning points to a maximum at the center, so the cards show the instantaneous Mach number. The wave speed is fixed: 150 px/s.
- “Uniform” mode: the source moves at a constant speed v = M·c and bounces off the edges. This is convenient for checking the picture against the formulas f₀ / (1 ∓ M) and the Mach cone.
- Stationary observers stand at the edges: when a wavefront reaches them, a ring flashes and the label shows the measured frequency. After the source turns around, they swap places between “in front” and “behind”.
- The yellow dots on the axis of motion are the points where wavefronts cross the flight line. In front they get closer together, behind they spread apart. You can turn them off with the checkbox.
Enter the source frequency, its speed and the observer’s speed to get the frequency the observer hears when approaching and receding.
Source frequency f₀, Hz
Source speed vs, m/s
Observer speed v₀, m/s
Wave speed in the medium c, m/s
Medium
Examples:
—
Frequency when approaching, Hz
—
Frequency when receding, Hz
—
Difference before and after, Hz
—
Source Mach number
—
Wavelength λ₀, m
Approaching: f′ = f₀ · (c + v₀) / (c − vs)
Receding: f′ = f₀ · (c − v₀) / (c + vs)
Receding: f′ = f₀ · (c − v₀) / (c + vs)
Typical source speeds in air (c = 343 m/s)
| M = v/c | v, m/s | f in front / f₀ | f behind / f₀ | Example |
|---|---|---|---|---|
| 0.1 | 34 | 1.11 | 0.91 | ≈ 123 km/h — high-speed train |
| 0.3 | 103 | 1.43 | 0.77 | ≈ 370 km/h — light aircraft |
| 0.5 | 172 | 2.00 | 0.67 | ≈ 617 km/h — turboprop aircraft |
| 0.7 | 240 | 3.33 | 0.59 | ≈ 864 km/h — passenger airliner |
| 0.9 | 309 | 10.00 | 0.53 | ≈ 1111 km/h — near the sound barrier |
| 1.0 | 343 | ∞ | 0.50 | Sound barrier: waves in front pile up into a shock wave |
Doppler Effect Online: Simulation and Calculator
A free interactive tool that shows clearly how the motion of a source changes the wavelength and frequency of a wave. The animation displays circular wavefronts from a moving source: in front they are compressed, behind they are stretched, and at speeds above the wave speed a Mach cone forms. A separate calculator computes the frequency shift for given source and observer speeds in air, water or any other medium.
Key concepts
Doppler shift
The difference between the frequency emitted by the source and the frequency perceived by the observer when they move relative to each other.
700 Hz → 767 Hz at v = 30 m/s
Mach number
The ratio of the source speed to the wave speed in the medium. For M < 1 the motion is subsonic, for M > 1 it is supersonic.
M = 1.4 → cone angle ≈ 45.6°
Redshift and blueshift
For light from receding galaxies the spectrum shifts toward red, and from approaching ones toward blue. This is how astronomers measure the speeds of stars and the expansion of the Universe.
Radial velocity of a star from the shift of its lines
Where it is used
- Radar and lidar for measuring the speed of cars and drones
- Doppler ultrasonography: blood flow speed in vessels and the heart
- Weather radars tracking the motion of rain clouds and wind
- Astronomy: redshift, searching for exoplanets by a star’s wobble
- Teaching wave physics at school and in the first year of university
- Understanding why the pitch of a siren, a train horn or a race car engine changes
How to use
- In the “Simulation” tab, move the speed slider and watch how the wavefronts get compressed
- Change the frequency to see how the overall density of the waves changes
- Try M = 1 and M = 1.4: you will see the shock wave and the Mach cone
- In the “Calculator” tab, enter the frequency, speeds and medium
- Copy the result with the button below
Frequently asked questions
What is the Doppler effect in simple words?
It is the change in the perceived frequency of a wave when the source and the observer move relative to each other. When the source approaches, the waves are “compressed” and the frequency rises (the sound is higher). When it recedes, the waves are “stretched” and the frequency drops (the sound is lower). That is why an ambulance siren changes its pitch as it drives past.
Why are the waves compressed in front of the source and stretched behind it?
The source emits each new wave crest from a different point in space. In front it “catches up” with its own waves, so the distance between crests decreases to (1 − v/c)·λ₀. Behind, it “runs away” from the waves, and the distance increases to (1 + v/c)·λ₀.
What happens when the source speed equals the wave speed?
The waves in front no longer get ahead of the source — all the crests pile up at a single point, forming a shock wave. The formula for the frequency in front diverges to infinity. For sound this is the sound barrier, and passing through it is accompanied by a sonic boom.
What is a Mach cone?
When the source moves faster than the waves, the circular wavefronts no longer enclose it but form a cone with its apex at the source. The half-angle at the apex α is given by sin α = 1/M, where M is the Mach number (the ratio of the source speed to the wave speed).
Does the calculator account for the observer’s motion?
Yes. Besides the source speed, you can enter the observer’s speed: then when approaching f′ = f·(c + v₀)/(c − v_s), and when receding f′ = f·(c − v₀)/(c + v_s). Everything is computed locally in your browser, and no data is sent anywhere.