Reverberant sound decays exponentially because wall absorption removes a fixed fraction of remaining energy

Evidence

Sabine discovered that the decay of sound was exponential. That is, after the first few bounces off the walls, sound energy tends to diminish exponentially over time once it is introduced into a room. Recall, in connection with damped oscillations and resonance (chapter 10), that exponential energy decay results if the amount of the energy removed in a given time interval is proportional to what remains. This seems reasonable for sound energy: the amount that escapes through an open window or is absorbed by walls, curtains, and the like is surely proportional to how much is impinging on these “absorbers.” — Eric J. Heller, Why You Hear What You Hear- An…, 2456

When a tone in the space stops, or after a transient, the reverberant sound level will not reduce immediately but will instead decay at a rate determined by the amount of sound energy that is absorbed at each reflection. Thus in spaces with a small amount of absorption the reverberant field will take longer to decay. — David Howard, Jamie Angus, coustics and Psychoacoustics, 1783

Categorization

• DEFINE: Explains the mechanism behind exponential sound decay in rooms — a foundational concept in architectural acoustics.
• XREF: This is the physical basis for tail-off quality in recordings — connects to how reverb tails are sculpted in audio production. — connects to: Mixed sound absorptions create multi-slope reverberant decay curves — David Howard, Jamie Angus, coustics and Psychoacoustics, 1900
• corroborated: 2 independent passages support this claim — Eric J. Heller, Why You Hear What You Hear- An…, 2456; David Howard, Jamie Angus, coustics and Psychoacoustics, 1783