Sound decays exponentially on reflection, but cyclic paths create standing waves

Evidence

When a room is excited by an impulse, the sound energy is reflected from its surfaces. At each reflection, some of the sound is absorbed, and therefore the sound energy decays exponentially. Ideally the sound should be reflected from each surface with equal probability, forming a diffuse field. This results in a single exponential decay with a time constant proportional to the average absorption in the room. However, in practice, not all the energy is reflected in a random fashion. Instead, some energy is reflected in cyclic paths, as shown in Figure 6.30. If the length of the path is a precise number of half wavelengths, they will form standing waves in the room. — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 1948

Categorization

• DEFINE: Defines the mechanism of exponential decay and the diffuse-field ideal before naming the standing-wave exception.
• DEEPTHINKING: A compact causal chain — reflection, absorption, exponential decay, then the geometry that breaks it — linking wave physics directly to what a listener hears as a room’s character.