Firework Shockwave: The Sound Delay (2D)

Burst Position

Distance from observer 800 m

Click anywhere on the map to move the firework there and launch it. Drag to pan, scroll/pinch to zoom.

Air Conditions

Air temperature 15 °C

Relative humidity 50%

Wind (advects the wavefront)

Wind speed 0 m/s

Wind direction 0°

Estimate the distance

Live Readouts

Speed of sound

340 m/s

Distance (top-down)

800 m

Predicted delay

2.35 s

Stopwatch

0.00 s

Your estimated distance

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Your error

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Press Launch to fire the shell.

Why the wavefront isn't a plain circle

This top-down map deliberately drops the burst's altitude — a genuine simplification, not the same model as the 3D version's slant-range geometry. Instead it adds something the 3D view doesn't model: wind. Sound propagates through the air itself, so a wind that's moving the whole body of air carries the wavefront along with it (advection). To first order, a uniform wind field just translates the wavefront's center by (wind × time) while it keeps expanding at v_sound relative to the moving air — so downwind the "circle" reaches you sooner than distance/v_sound predicts, and upwind it's later. Solving |observer − burst − wind·t| = v_sound·t for t is a quadratic in t; this simulation solves it exactly every frame rather than approximating, so the delay you read off is the true root of that equation, not just distance/v_sound with a fudge factor.

Observer: you, map center
Burst: 800 m away