Reflected sound obeys an inverse square law in addition to surface absorption losses

Evidence

Equation 6.16 gives us the time between surface interactions, and at each of these interactions, α is the proportion of the energy absorbed, where α is the average absorption coefficient discussed earlier. If α of the energy absorbed at the surface, then (1 − α) is the proportion of the energy reflected back to interact with further surfaces. At each surface a further proportion, α, of energy will be removed, so the proportion of the original sound energy that is reflected will reduce exponentially. The combination of the time between reflections and the exponential decay of the sound energy, through progressive interactions with the surfaces of the room, can be used to derive an expression for the length of time that it would take for the initial energy to decay by a given ratio. — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 1830 (#qualifies, via linked claim)

What is the 60 dB reverberation time (T60) of a living room as a function of frequency whose surface area is 75 m2 and whose volume is 42 m3? The floor is carpet on concrete, the ceiling is plaster on lath, and both have an area of 16.8 m2. There are 6 m2 of windows and the rest of the surfaces are painted plaster on brick; ignore the effect of the door. Using the data in Table 6.1, set up a spreadsheet or table, as shown in Table 6.2, and calculate the equivalent open window area for each surface as a function of frequency. Having done that add up the individual surface contributions for each frequency band and apply Equation 6.20 to the result in order to calculate the reverberation time. — David Howard, Jamie Angus, coustics and Psychoacoustics, 1929 (#qualifies, via linked claim)

If a steady tone, such as an organ note, is played in the space then after a period of time the reverberant sound will reach a constant level because at that point the sound power input balances the power lost by absorption in the space. This means that the steady-state level will be higher in rooms that have a small amount of absorption, compared with rooms that have a lot of absorption. — David Howard, Jamie Angus, coustics and Psychoacoustics, 1781 (#qualifies, via linked claim)

Categorization

• XREF: connects to: In rooms the inverse-square law applies only to the direct sound — Toole, Floyd E, Sound reproduction- the acoustics and…, 1260; Reflected sound fields dominate at low frequencies for almost all sources — , Toole, Floyd E - Sound reproduction-…, 1213; Inverse-square law governs direct sound intensity even inside enclosed spaces (+7 more)

Broader Connections

• Room sound energy decays exponentially through repeated surface absorptions #qualifies (0.85) — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 1830
• Total surface area can outweigh absorption efficiency in controlling room reverberation #qualifies (0.82) — David Howard, Jamie Angus, coustics and Psychoacoustics, 1929
• Room absorption determines the steady-state level of reverberant sound #qualifies (0.80) — David Howard, Jamie Angus, coustics and Psychoacoustics, 1781