Sound in a room

Seen from above · click anywhere in the room to clap

Room

Play through the room

What's going on

Clap in a small studio and then in a cathedral and you hear two very different rooms. The clap is the same; the walls are not. Sound spreads like ripples on water and bounces off every surface: a room lined with foam swallows the reflections, a stone cathedral keeps them ringing for seconds.

What you hear in any room is the sound itself, then a few clear echoes from the nearest walls, then thousands of later reflections that blur into a tail: the reverb. How long it lasts depends on how big the room is and how hard its walls are.

Why it matters: a room shapes music as much as the instruments do. Studios, concert halls and headphones that imitate rooms all start from these physics, and removing a room's echo from a recording is an active research problem in audio machine learning.

The maths behind itFor the curious · formulas and details

The simulation

Sound pressure p obeys the wave equation, with c ≈ 343 m/s in air:

∂²p/∂t² = c² · ∇²p

The picture solves it on a 180 × 120 grid with finite differences: each cell's next value comes from its current and previous values and its four neighbours. Walls are held at zero, so waves reflect; cells next to a wall lose a little energy each step (more for soft surfaces), and a little is lost to the air everywhere. The time step is chosen so the scheme stays stable.

Reverberation time

RT₆₀ is the time for the sound to fade by 60 dB, to a millionth of its energy. Sabine's formula relates it to the room's volume V (m³) and total absorption A (m², each surface's area times its absorption coefficient):

RT₆₀ ≈ 0.161 · V / A

The audio uses a synthesized impulse response per room (a few early reflections and a noise tail that decays by 60 dB over RT₆₀), applied to the clap or the beat by convolution.