Doppler Effect Simulator

Verified Content: All equations, formulas, and reference data in this simulation have been verified by the Simulations4All engineering team against authoritative sources including MIT OpenCourseWare physics courses, HyperPhysics, and NASA educational resources. See verification log

Introduction

You know that sound. The ambulance coming down the street with its high-pitched wail, then passing you, and suddenly the siren drops to a lower moan. Same ambulance, same siren, same physical mechanism making the sound. So why does the pitch change so dramatically in that split second as it passes?

Here's what happens when you actually try this: stand on a street corner and listen carefully as a car with a loud engine approaches. The pitch rises as it gets closer, stays constant as it's right beside you (for that brief moment when it's neither approaching nor receding), then falls as it drives away. What Doppler figured out in 1842 was that this isn't some trick of perception or acoustic illusion [1]. The waves themselves are genuinely bunched up in front of a moving source and stretched out behind it. Your ears are telling you the truth.

The elegant part is that this exact same physics governs how astronomers measure the speeds of distant galaxies, how police radar guns catch speeders, and how doctors can watch blood flowing through your arteries without making a single cut. Our simulator lets you manipulate both sound and light waves, watching in real time as motion compresses or stretches the wave fronts. You can even push a source past the speed of sound and watch the Mach cone form. Isn't it remarkable that one simple idea connects ambulance sirens to the expansion of the universe?

What Is the Doppler Effect?

Imagine you're in a boat on a calm lake, and a friend starts throwing tennis balls at you at a steady rate, one per second. If your friend stands still, balls arrive at one per second. Now imagine your friend walks toward you while throwing. Each ball is released from a closer position than the last. The balls still travel at the same speed through the air, but they arrive faster than one per second because the gap between throws has effectively shrunk [2].

The elegant part is that waves work the same way. A sound source vibrates at a fixed frequency, sending out wave crests at regular intervals. If you could slow this down enough to watch, you'd see each crest leaving the source and expanding outward like ripples from a stone dropped in water. When the source moves, it chases its own wave crests in the forward direction, bunching them together. Behind the source, it runs away from the crests, spreading them apart.

What changes is not the wave speed (that depends only on the medium) and not the source frequency (the source keeps vibrating at the same rate). What changes is the wavelength, and therefore the frequency that reaches an observer. The approaching side receives compressed waves at higher frequency. The receding side receives stretched waves at lower frequency. The source is completely unaware this is happening. It just keeps emitting waves at its natural frequency, oblivious to what observers at different positions perceive.

How the Simulator Works

The visualization shows wave fronts expanding from the source position. Watch how they bunch up in front of an approaching source. The status display calculates observed frequency in real time using the classical or relativistic formula depending on whether you've selected sound or light mode.

Technical Deep-Dive: The Mathematics of Frequency Shift

Classical Doppler Effect for Sound

Here's what happens when you actually try this with a moving sound source. The classical Doppler formula is [3]:

f' = f × (v + v_o) / (v − v_s)

Where:

• f' = frequency the observer perceives
• f = frequency the source emits
• v = speed of sound in the medium (343 m/s in air at 20°C)
• v_o = observer velocity (positive when moving toward source)
• v_s = source velocity (positive when moving toward observer)

Why this particular form? Think about the denominator. If the source approaches at v_s, the effective distance between wave crests shrinks by the factor (v − v_s)/v. That means wavelength compresses, so frequency goes up. The numerator handles observer motion similarly. If you run toward the source, you encounter crests faster than if you stood still.

Here's an important subtlety that physics students often miss: source motion and observer motion don't produce identical effects for sound. A source approaching at 30 m/s gives a different frequency shift than an observer approaching at 30 m/s. Why? Because sound waves propagate through a medium (air), and the medium defines a preferred reference frame. Moving relative to that medium matters differently depending on whether you're the source or the observer.

The Mach Number: When Sources Outrun Their Waves

What Doppler figured out was that something dramatic happens when a source reaches the wave speed. The Mach number is simply [4]:

M = v_s / v

At M = 1, the source travels exactly at the speed of sound. The wave crests pile up in front of it, unable to escape ahead. They accumulate into a pressure wall. Push the source faster, to M > 1, and something geometrically inevitable happens: the source outruns all its waves. Every crest the source has ever emitted now lies within a cone behind it.

The half-angle of this Mach cone is:

sin(theta) = 1/M

At Mach 2, theta equals 30 degrees. At Mach 3, about 19.5 degrees. The faster you go, the sharper the cone. When this cone sweeps past an observer, they experience a sonic boom, the sudden arrival of all those accumulated pressure waves at once. The universe doesn't care about our intuition, but this is exactly why a supersonic jet doesn't sound like a whooshing approach and departure. You hear nothing, then BOOM, then the sound of it receding.

Relativistic Doppler Effect for Light

Light doesn't need a medium. It propagates through empty space at exactly c = 299,792,458 m/s, and Einstein showed that this speed is the same for all observers regardless of their motion [5]. This changes the Doppler formula significantly. Time dilation enters the picture.

The relativistic Doppler formula for an observer and source with relative velocity v is:

f' = f x sqrt((1 - beta) / (1 + beta))

Where beta = v/c is the velocity as a fraction of light speed. The square root captures the time dilation factor. Unlike sound, there's no distinction between source motion and observer motion. Only the relative velocity matters because there's no medium to define a preferred frame.

For a receding source (positive beta), this gives f' < f: redshift. For an approaching source (negative beta), f' > f: blueshift. At v = 0.6c (60% of light speed), the frequency drops to half. At v = 0.9c, it drops to about 23% of the original. These are massive shifts, and astronomers see them all the time in quasars and jets from active galactic nuclei.

Connecting Wavelength and Frequency

Whatever happens to frequency, wavelength changes in the opposite direction. Since wave speed equals frequency times wavelength (v = f x lambda), compressing frequency means stretching wavelength, and vice versa. For light, redshift means longer wavelengths (toward the red end of the visible spectrum). Blueshift means shorter wavelengths (toward blue). But don't confuse this with the object actually appearing red or blue. The shift is relative to the object's emitted spectrum. A star that naturally emits blue light could be redshifted and still look blue, just less blue than it should be.

Learning Objectives

After working through this simulation, you should be able to:

1. Explain why the pitch of a siren changes as an ambulance passes, distinguishing the compression of approaching waves from the stretching of receding waves
2. Calculate observed frequency using the classical Doppler formula, correctly handling sign conventions for source and observer velocities
3. Predict whether a given motion scenario will produce a frequency increase or decrease before running the calculation
4. Define the Mach number and explain geometrically why a shock wave cone forms at supersonic speeds
5. Apply the relativistic Doppler formula to astronomical scenarios, understanding why time dilation modifies the classical result
6. Relate redshift measurements to galaxy recession velocities and the expansion of the universe

Exploration Activities

Activity 1: The Ambulance That Changed Pitch

Objective: Reproduce the classic experience of a siren passing by

Steps:

1. Select Sound Waves mode and click the Ambulance preset
2. Press Play to watch the waves propagate
3. Notice how the wave fronts crowd together in the direction of motion
4. Read the observed frequency, it should be higher than the source frequency of 700 Hz
5. Now change the source velocity slider to -30 m/s (receding instead of approaching)
6. Watch the wave fronts spread apart behind the source
7. Compare the new observed frequency to the original

What to Look For: The frequency jump when switching from approaching to receding represents that dramatic pitch drop you hear as an ambulance passes. In the real world, this transition happens smoothly as the vehicle's velocity component toward you changes from positive to negative.

Activity 2: Racing to Break the Sound Barrier

Objective: Watch what happens as a source approaches and then exceeds Mach 1

Steps:

1. Start with source velocity at 0 m/s
2. Slowly increase velocity while watching the Mach number display
3. At around 300 m/s (Mach ~0.87), observe how crowded the wave fronts become ahead of the source
4. Push to 343 m/s (Mach 1) and watch the waves pile up into a flat wall in front
5. Select the Supersonic preset (Mach 1.5) to see the fully formed Mach cone
6. Note how the cone angle changes if you adjust velocity higher or lower

What to Look For: The transition at Mach 1 is the dramatic part. Below it, waves still escape ahead. At exactly Mach 1, they can't escape. Above it, the source has outrun everything it ever emitted.

Activity 3: Redshift and the Expanding Universe

Objective: Understand how astronomers discovered cosmic expansion

Steps:

1. Switch to Light Waves mode
2. Select the Distant Galaxy preset
3. Observe the color spectrum bar showing the shift toward red
4. Note the substantial drop in observed frequency (you're seeing electromagnetic radiation redshifted by cosmic recession)
5. Switch to the Approaching Star preset and compare
6. Try intermediate velocities and watch how the shift scales with velocity

What to Look For: Edwin Hubble noticed that virtually all distant galaxies show redshift, and farther galaxies show more [6]. The elegant part is that this pattern means the universe is expanding. Everything is receding from everything else. The Doppler effect became a ruler for measuring cosmic velocities.

Activity 4: Does the Medium Matter?

Objective: Explore why wave speed affects frequency shift

Steps:

1. In Sound mode, set source velocity to exactly 30 m/s approaching
2. With Air selected (343 m/s), record the percentage frequency shift
3. Change to Water (1480 m/s) and record the new shift
4. Change to Helium (970 m/s) and record again
5. Calculate v_s/v for each case and compare to the frequency shift

What to Look For: Higher wave speeds mean the source velocity is a smaller fraction of wave speed. At 30 m/s in air, you're moving at about 8.7% of the wave speed. In water, only 2%. The denominator (v − v_s) changes less when v is much larger than v_s, so the frequency shift shrinks.

Real-World Applications

Radar Speed Guns and Traffic Enforcement

When a police officer aims a radar gun at your car, they're firing microwave radiation at known frequency. The waves bounce off your car and return. If you're moving toward the radar, the reflected waves are blueshifted, compressed by your approach. The gun measures this shift and calculates your speed instantly [7]. The physics is identical to the ambulance siren, just at electromagnetic frequencies instead of acoustic ones.

Medical Doppler Ultrasound

Doctors routinely watch blood flow in real time without any invasion of the body. High-frequency sound waves bounce off red blood cells. Moving blood cells shift the return frequency. By mapping these shifts across a blood vessel, cardiologists can measure flow velocity, detect blockages, and identify abnormal circulation [8]. Fetal heart monitors use the same principle to pick out a baby's heartbeat from surrounding tissue.

Weather Radar and Tornado Detection

Doppler radar revolutionized severe weather forecasting. By measuring the frequency shift of radar returns from rain and hail, meteorologists see not just where precipitation is, but how fast and in what direction it's moving [9]. Rotation signatures in supercell thunderstorms, where one side approaches while the other recedes, are the telltale sign of tornado formation. The warning time this provides has saved countless lives.

Astronomical Redshift and Cosmology

In 1929, Edwin Hubble compiled redshift measurements from dozens of galaxies and found a remarkable pattern: the farther away a galaxy, the faster it recedes [6]. This Hubble Law became the foundation of modern cosmology. We now know the universe began in a Big Bang about 13.8 billion years ago and has been expanding ever since. Every measurement of cosmic expansion depends on the Doppler effect.

Sonar and Submarine Detection

Sound travels excellently through water (roughly four times faster than in air). Submarines and ships use active sonar to send out acoustic pulses and listen for returns. Moving objects shift the return frequency. Even passive sonar, just listening, can extract target velocity from the Doppler shift of propeller noise or hull vibrations. Navies have built entire tactical systems around this principle.

Reference Data: Speed of Sound in Different Media

Challenge Questions

Question 1 (Starter): An ambulance approaches at 30 m/s with a siren frequency of 700 Hz. The speed of sound is 343 m/s. What frequency does a stationary observer hear?

Hint: Use f' = f × v/(v − v_s) with positive v_s since the source approaches.

Question 2 (Starter): Does the Doppler effect physically change the frequency that the source emits, or does it only affect what an observer perceives?

Think about what the source mechanism is actually doing versus what reaches different observers.

Question 3 (Intermediate): A jet flies at Mach 2.5. What is the half-angle of its Mach cone?

Hint: Use sin(theta) = 1/M and solve for theta.

Question 4 (Intermediate): A distant star emits light at 600 THz (visible orange-red). It recedes at 10% the speed of light. Using the relativistic formula, what frequency do we observe?

Hint: Use f' = f x sqrt((1 - 0.1)/(1 + 0.1)) and compute.

Question 5 (Advanced): Two identical tuning forks emit 440 Hz. One approaches you at 10 m/s while the other recedes at 10 m/s. What beat frequency do you hear? (Speed of sound = 343 m/s)

Calculate both observed frequencies separately, then find their difference.

Common Misconceptions

Frequently Asked Questions

Why does the siren pitch drop so suddenly when an ambulance passes me?

Here's what happens when you actually try this: as the ambulance approaches, your velocity component relative to you is positive, and the waves compress (higher pitch). As it recedes, that component becomes negative, and waves stretch (lower pitch). The transition from positive to negative happens instantly at the moment it passes, which is why the pitch seems to drop suddenly rather than gradually [2]. If the ambulance drove in a circle around you, the pitch would rise and fall smoothly as it alternated between approaching and receding.

How did Hubble discover the universe was expanding using redshift?

Edwin Hubble measured spectral lines from dozens of galaxies and found nearly all of them redshifted. More remarkably, the amount of redshift correlated with distance: farther galaxies receded faster [6]. This Hubble Law (v = H_0 x d) implied the universe is expanding uniformly in all directions. Wind the cosmic movie backward, and everything converges to a single point, the Big Bang. The Doppler effect became humanity's tape measure for the cosmos.

Can I experience the Doppler effect with light in everyday life?

In principle yes, but the shifts are imperceptibly small at everyday speeds. A car moving at 30 m/s shifts visible light by about 0.00001% in frequency. You'd need specialized equipment to detect it. Astronomers see large redshifts because cosmic objects move at thousands or millions of kilometers per second. Relativistic effects become noticeable only above roughly 1% of light speed [5].

What exactly happens at the speed of sound?

At Mach 1, the source moves exactly as fast as its own waves. Wave crests emitted ahead can never escape because the source keeps pace with them. They pile up into a pressure wall perpendicular to the direction of motion [4]. Pilots breaking the sound barrier feel buffeting from this accumulated pressure. Once through, the aircraft outruns everything and the pressure wall transforms into the Mach cone trailing behind.

Why do we need a different formula for light compared to sound?

Sound travels through air (or water, or whatever medium). That medium defines a reference frame. Whether the source moves through the air or the observer moves through the air produces slightly different effects. Light, however, travels through empty space at exactly c for all observers, regardless of their motion [5]. Einstein showed this constancy of light speed requires modifying the formula to account for time dilation. The relativistic Doppler formula handles both source and observer motion identically because only relative motion matters when there's no medium.

References

1. Doppler, C. (1842). On the Coloured Light of the Binary Stars and Some Other Stars of the Heavens. Proceedings of the Royal Bohemian Society of Sciences. Historical context available at: https://www.aps.org/publications/apsnews/200603/history.cfm

2. MIT OpenCourseWare. 8.03SC Physics III: Vibrations and Waves. Module on Doppler Effect. Massachusetts Institute of Technology. Available at: https://ocw.mit.edu/courses/8-03sc-physics-iii-vibrations-and-waves-fall-2016/

3. HyperPhysics. The Doppler Effect. Georgia State University Department of Physics and Astronomy. Available at: http://hyperphysics.phy-astr.gsu.edu/hbase/Sound/doppler.html

4. NASA Glenn Research Center. Speed of Sound and Mach Number. Glenn Research Center Educational Resources. Available at: https://www.grc.nasa.gov/www/k-12/airplane/sound.html

5. Einstein Online. The Relativistic Doppler Effect. Max Planck Institute for Gravitational Physics. Available at: https://www.einstein-online.info/en/spotlight/doppler/

6. NASA Science. Hubble's Law and the Expanding Universe. NASA Goddard Space Flight Center. Available at: https://science.nasa.gov/universe/overview/

7. NIST. Radar Speed Measurement and Calibration. National Institute of Standards and Technology Law Enforcement Standards Laboratory. Available at: https://www.nist.gov/

8. American Heart Association. Echocardiography and Doppler Ultrasound. Heart.org Patient Education. Available at: https://www.heart.org/en/health-topics/heart-attack/diagnosing-a-heart-attack/echocardiogramechocardiography

9. NOAA National Weather Service. How Doppler Radar Works. JetStream Online School for Weather. Available at: https://www.weather.gov/jetstream/doppler

10. Engineering ToolBox. Speed of Sound in Various Media. Reference tables for acoustic properties. Available at: https://www.engineeringtoolbox.com/sound-speed-solids-d_713.html

11. Acoustical Society of America. Standards for Human Hearing Range. Available at: https://acousticalsociety.org/

12. NIST CODATA. Recommended Values of Fundamental Physical Constants. Speed of light defined value. Available at: https://physics.nist.gov/cuu/Constants/

13. Open University. The Doppler Effect in Astronomy. OpenLearn free educational resources. Available at: https://www.open.edu/openlearn/

About the Data

All wave speeds in this simulation come from standard physics reference tables verified against NIST standards and peer-reviewed sources. The speed of sound in air (343 m/s) applies at 20C and standard atmospheric pressure; actual values vary with temperature according to v = 331 + 0.6T where T is Celsius. Water and helium values likewise assume standard conditions. The speed of light is exact by SI definition at 299,792,458 m/s. Ambulance siren frequencies (650-750 Hz) represent typical ranges for US emergency vehicles. Human hearing boundaries (20-20,000 Hz) define the practical limits for acoustic Doppler observations.

How to Cite

Simulations4All. (2026). Doppler Effect Simulator: Interactive exploration of frequency shifts in sound and light waves. Simulations4All Physics Collection. Retrieved from https://simulations4all.com/simulations/doppler-effect-simulator

For academic use:

Simulations4All Team. "Doppler Effect Simulator." Simulations4All, 2026, simulations4all.com/simulations/doppler-effect-simulator. Accessed [date].

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