The Doppler effect
About this app
Move a sound source and compare compressed and stretched wavefronts. Explore observed frequency, audible pitch changes and the Mach cone beyond sound speed.
With explain mode: an AI tutor walks you through the app, points out what matters in the scene and answers your questions.
Why the pitch changes
A sound source emits wavefronts at equal time intervals, which spread out as circles at the speed of sound c. If the source moves with speed v, the fronts bunch up ahead of it and spread out behind it. A stationary listener in front therefore hears a higher frequency and one behind a lower frequency: f′ = f · c / (c ∓ v), with minus when approaching and plus when receding.
What the app shows
A moving source emits visible wavefronts. Two observers, one in front and one behind, show the received frequency f′, together with the source frequency f and the Mach number v/c. You set the source speed and source frequency with sliders. Optionally the sound for both observers becomes audible at constant volume, so that only the pitch differs.
Supersonic speed and the Mach cone
Push v above the speed of sound: the source overtakes its own wavefronts, and the circles pile up into a cone-shaped envelope, the Mach cone with sin θ = c/v. The observer in front then receives no sound until the cone arrives. At that moment many fronts arrive at once, which is the sonic boom.
Frequently asked questions
- What is the Doppler effect?
- The Doppler effect is the change in the observed frequency of a wave when source and observer move relative to each other. An approaching source sounds higher, a receding one lower. The classic example is the siren of a passing ambulance.
- What is the Doppler formula for a moving source?
- For a stationary observer and a moving source, f′ = f · c / (c − v) when approaching and f′ = f · c / (c + v) when receding. Here f is the emitted frequency, c the speed of sound and v the speed of the source.
- Does the Doppler effect make a sound louder or higher?
- The Doppler effect changes the pitch, not the loudness. A source that approaches also gets louder because it is closer, but that is a separate effect. As it passes, the pitch drops from high to low while the loudness rises and falls smoothly.
- What does the simulator show?
- It shows the wavefronts of a moving sound source, the received frequency for an observer in front and behind, and the Mach cone at supersonic speed. Speed and frequency are adjustable, and you can listen to the tone.
Subject: School physics
More from School physics
- The exposure triangle
- Density and buoyancy
- Additive and subtractive colour mixing
- Newton’s cradle and collisions
- Converging lenses and ray diagrams
- Projectile motion
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