Doubling a room’s dimensions doubles its reverberation time

Evidence

We should not stop here—does the law of similarity apply when we include absorbing walls and decay of the sound? T60 depends on the ratio of volume to surface area. If we scale the room up or down by a factor of η, the volume changes by a factor η3, and the surface area, by a factor η2, meaning that T60 will scale as η. We assume the scaling does not affect α. Thus, if a room doubles in its linear dimensions, T60 will increase by a factor of 2. We do not have to look far to find the reason: the time spent in flight between collisions with walls does not reduce the sound energy. There are fewer collisions per second—in fact, exactly a factor of 2 in our example of doubling the room dimensions—so it takes twice as long for the sound to die down. We have shown that the law of similarity applies even if there is absorption of sound. — Eric J. Heller, Why You Hear What You Hear- An…, 2495

Categorization

• XREF: Clean scaling law with the mechanical intuition (fewer wall collisions per second) — connects to why large halls need absorbent treatment to keep reverberation under control.