Firework Shockwave: The Sound Delay (3D)

Burst Geometry

Distance from observer 800 m

Burst altitude 150 m

Click anywhere on the ground to move the firework there and launch it instantly.

Air Conditions

Air temperature 15 °C

Relative humidity 50%

Estimate the distance

Watch the flash, then click the button the instant you think you hear the boom — like counting seconds after lightning.

Live Readouts

Speed of sound

340 m/s

Straight-line distance

815 m

Predicted delay

2.40 s

Stopwatch

0.00 s

Your estimated distance

—

Your error

—

Press Launch to fire the shell.

Why the delay is real

Light from the burst covers the ~1 km line of sight in about 3 microseconds — for any distance you'd use for a firework, that's indistinguishable from instant. Sound, a pressure wave carried by colliding air molecules, is nearly a million times slower: v ≈ 331.3 + 0.606·T(°C) m/s near sea level, so warmer air actually carries sound faster (faster molecular motion, more collisions per second), and a small secondary term accounts for humid air being slightly less dense than dry air. The wavefront you see expanding is a physically-scaled sphere growing at exactly that speed from the true 3D burst point — when its radius equals the straight-line (slant) distance to you, delay = distance / v_sound seconds have passed, and the "boom" arrives. This is exactly the rule behind counting seconds after a lightning flash to estimate the storm's distance (≈ 343 m per second, or roughly one mile per five seconds).

Observer: you, at the camera target
Burst: 800 m away, 150 m up

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