Scivra

Preview

Doppler Effect

Observe frequency shifts as source and observer move relative to each other

An ambulance tears past you and the siren drops a full step the instant it goes by — yet the medic behind the wheel hears the same unwavering wail the entire ride. Nothing about the siren changed. What changed is the spacing of the wavefronts: as the source chases its own sound, each new crest is born a little closer to the previous one ahead of it, and a little farther behind. Crests crowd together in front, stretch apart in back, and your ears read that crowding as pitch. The same bookkeeping runs on any wave: radar guns clock traffic, ultrasound images blood flow, and astronomers weigh the expansion of the universe in the stretched light of fleeing galaxies. In this lab you will stack wavefronts with your own hands, shove a source through the sound barrier at 343 m/s, and watch a frequency readout race to infinity as the Mach cone forms.

What you'll be able to do

  • Explain that a wave's frequency is set by the source and its speed by the medium — a moving siren still emits f_s while sound travels 343 m/s in air regardless of source motion
  • Apply f_obs = f_s·(v ± v_obs)/(v ∓ v_s) to predict observed frequency for approaching and receding source/observer combinations
  • Describe what happens as source speed reaches and exceeds the wave speed: wavefront pile-up, the divergence of the ahead-frequency, and the Mach cone (M = v_s/v_sound)

Formulas

fobs=fs⋅v±vobsv∓vsf_{obs} = f_s \cdot \frac{v \pm v_{obs}}{v \mp v_s}
Doppler formula: upper signs when source/observer approach, lower signs when receding
M=vsvsoundM = \frac{v_s}{v_{sound}}
Mach number: ratio of source speed to sound speed
λfront=v−vsfs\lambda_{front} = \frac{v - v_s}{f_s}
Compressed wavelength in front of a moving source

Make a prediction

Load the Ambulance Siren preset: the siren emits 700 Hz and drives toward the observer at 25 m/s (speed of sound 343 m/s). Before you peek at the panel — what does the f_obs (ahead) readout show, and what is the siren itself emitting?

No grading here — commit to a guess, then scroll down and test it yourself.

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Check

Did the lab agree with you?

Your prediction

You skipped the prediction — jump back to the preview and commit to a guess first; the comparison is the whole point.

Answer: f_obs (ahead) reads about 755 Hz, while the siren keeps emitting exactly 700 Hz — wavefronts ahead are born crowded closer together, so more crests reach the observer each second

The siren's mechanism vibrates at 700 Hz no matter how the ambulance moves — the f_source row stays pinned at 700 Hz for the whole run, and the comoving driver hears 700 Hz. What motion changes is geometry: every 1/700 s a new crest leaves a source that has moved 25/700 m closer to the observer, so ahead of the source the wavelength compresses to λ = (343−25)/700 ≈ 0.454 m and crests arrive at f_obs = f_s·v/(v−v_s) = 700×343/318 ≈ 755 Hz. Behind the source the same logic stretches the wave: λ ≈ 0.526 m and f_obs = 700×343/368 ≈ 652 Hz. The panel shows all three at once — 700 Hz emitted, ≈755 Hz heard ahead, ≈652 Hz heard behind — three numbers from one unchanging siren.

Quiz (0/3)

An ambulance moves toward an observer at 30 m/s with a siren at 800 Hz. What frequency does the observer hear? (v_sound = 343 m/s)

The same ambulance is now moving away. How does the observed frequency compare to the source frequency?

What happens to the wavefront pattern when source speed exactly equals the speed of sound (Mach 1)?

You can now

  • Explain that a wave's frequency is set by the source and its speed by the medium — a moving siren still emits f_s while sound travels 343 m/s in air regardless of source motion
  • Apply f_obs = f_s·(v ± v_obs)/(v ∓ v_s) to predict observed frequency for approaching and receding source/observer combinations
  • Describe what happens as source speed reaches and exceeds the wave speed: wavefront pile-up, the divergence of the ahead-frequency, and the Mach cone (M = v_s/v_sound)

What you'll learn

  • Wave Compression Ahead. When a source moves toward you, each successive wavefront is emitted from a position closer to you. The wavefronts pile up, shortening the wavelength and raising the frequency you hear. This is why an approaching siren sounds higher-pitched.
  • The Doppler Formula. The observed frequency depends on both the source speed and the wave speed in the medium. When the source approaches, the denominator shrinks, increasing the observed frequency. When it recedes, the denominator grows, decreasing it.
  • Breaking the Sound Barrier. At Mach 1, the source travels as fast as its own sound waves. All wavefronts pile up at a single point, creating a massive pressure spike — the sonic boom. Beyond Mach 1, the source outruns its wavefronts, forming a cone-shaped shock wave.
  • Doppler in Real Life. Radar speed guns bounce microwaves off moving cars and measure the frequency shift. Doppler ultrasound measures blood flow velocity. Astronomers use redshift to determine that distant galaxies are moving away from us — evidence for the expanding universe.
  • Medium Matters. The Doppler effect depends on the speed of sound in the medium. Sound travels at 343 m/s in air but 1,480 m/s in water. The same source speed produces a much smaller frequency shift in water because the waves travel so much faster relative to the source. This simulation uses air (343 m/s) throughout.

Step-by-step

  1. Set source frequency (try 440 Hz — concert A) and drag the source speed slider.
  2. The circular wavefronts animate in real time showing compression ahead (blue) and expansion behind (orange).
  3. The data panel displays the observed frequency ahead of and behind the source, both wavelengths, and the Mach number.
  4. Enable the Pro observer-velocity control to set the observer in motion, or use the presets — Ambulance Siren, Supersonic (Mach 1.2), and Moving Observer.

Key formulas

  • fobs=fs⋅v±vobsv∓vsf_{obs} = f_s \cdot \frac{v \pm v_{obs}}{v \mp v_s}Doppler formula: upper signs when source/observer approach, lower signs when receding
  • M=vsvsoundM = \frac{v_s}{v_{sound}}Mach number: ratio of source speed to sound speed
  • λfront=v−vsfs\lambda_{front} = \frac{v - v_s}{f_s}Compressed wavelength in front of a moving source

Frequently asked questions

An ambulance moves toward an observer at 30 m/s with a siren at 800 Hz. What frequency does the observer hear? (v_sound = 343 m/s).
The correct answer is: ≈ 877 Hz. Observer stationary, source approaching: f_obs = f_s × v / (v − v_s).
The same ambulance is now moving away. How does the observed frequency compare to the source frequency?
The correct answer is: Lower than 800 Hz. Source receding: f_obs = f_s × v / (v + v_s). Is it higher or lower than 800 Hz?
What happens to the wavefront pattern when source speed exactly equals the speed of sound (Mach 1)?
The correct answer is: Wavefronts pile up at one point creating a shock wave. All wavefronts accumulate at the same point. What physical phenomenon does this produce?