Room Reverberation and Image Sources

Reverberation is thousands of tiny echoes

When a sound is made in a room, only a fraction of the acoustic energy reaches a listener directly. The rest bounces off walls, ceiling and floor, arriving from many directions and at many different times, each bounce weaker than the last because every reflective surface absorbs some fraction of the energy that hits it. The listener perceives this dense, decaying wash of arrivals as reverberation, and it is the single biggest factor separating a "live," echoey room from a "dead," acoustically treated one.

The image-source method: unfolding reflections into ghost rooms

For a room with flat, rigid walls, there is an elegant trick for computing early reflections exactly: a reflection off a wall looks geometrically identical to sound arriving in a straight line from a mirror-image source, reflected through that wall's plane. Mirror the original source across every wall to get first-order image sources, then mirror each of those across every wall again for second-order images, and so on. Each image source, traced back through the correct sequence of walls, gives the exact path length, arrival time and cumulative absorption of one specific reflection.

order 0:  direct sound, straight line, source to listener
order 1:  one wall bounce, 6 image sources for a rectangular room
order 2:  two wall bounces, up to 30 image sources
order N:  reflection count grows roughly as 6*(5^(N-1))

each image source contributes: delay = path_length / speed_of_sound
                                level = 1/path_length * (wall absorption)^bounces

The image-source method is exact for rectangular rooms with hard walls and becomes an efficient approximation for irregular ones, and it is exactly what produces the crisp early-reflection pattern a listener uses to judge a room's size before the reverberant tail even builds up.

live demo · a sound wave decaying through reflections● LIVE

RT60: one number for the whole decay

Tracing every individual reflection is exact but unwieldy for describing a room in a single spec. RT60 — reverberation time — condenses the whole decaying tail into the time it takes reverberant sound pressure to fall by 60 decibels after the source stops, roughly the difference between a loud shout and inaudibility. Wallace Clement Sabine derived the first practical formula for it in 1898 while consulting on the disastrously reverberant lecture hall at Harvard's Fogg Museum, founding architectural acoustics as a quantitative discipline in the process.

Sabine:  RT60 = 0.161 * V / A                (metric, RT60 in seconds)

V  = room volume (cubic metres)
A  = total absorption = sum over every surface of (area * absorption coefficient)

Sabine versus Eyring: where the simple formula breaks

Sabine's formula is a statistical approximation that assumes sound energy is diffuse and absorption is fairly low, and it works remarkably well for typical rooms. But it has an odd flaw: it predicts a nonzero RT60 even when every surface has an absorption coefficient of 1, meaning a room that should absorb all sound on the first bounce. Carl Eyring's 1930 correction replaces the linear absorption term with a logarithmic one, which correctly drives RT60 to zero in that limit and tracks measured reverberation more accurately in heavily damped spaces such as recording studios and anechoic-adjacent rooms:

Eyring:  RT60 = 0.161 * V / (-S * ln(1 - avg_alpha))

S          = total surface area
avg_alpha  = area-weighted average absorption coefficient

In practice, acousticians use Sabine for quick estimates in moderately live rooms and switch to Eyring once average absorption climbs much past 0.2 to 0.3, where the two formulas start to visibly diverge.

Frequently asked questions

What RT60 is considered good for a room?

It depends entirely on the room's purpose. Speech spaces like classrooms and offices target roughly 0.4 to 0.6 seconds for intelligibility, concert halls for orchestral music aim for a richer 1.8 to 2.2 seconds, and recording studios push well under 0.3 seconds so the room itself stays nearly inaudible.

Why do empty rooms echo more than furnished ones?

Furniture, carpet, curtains and people all add absorption area with typically high absorption coefficients. An empty room's Sabine absorption is dominated by hard, reflective surfaces with low coefficients, so its RT60 is longer, and long reverberation is exactly what listeners perceive as echoey or boomy.

Do the Sabine and Eyring equations ever disagree noticeably?

Yes, most noticeably in very absorptive rooms. Sabine's equation is a linear approximation that becomes physically impossible at very high absorption, predicting a small but nonzero RT60 even for a room whose average absorption coefficient equals 1. Eyring's logarithmic correction handles that limit correctly and the two converge closely for moderately live rooms.

Try it live

Everything above runs in your browser — open Room Acoustics and RT60 Reverberation Time and change the parameters while it is running. Nothing is installed, nothing is uploaded, the whole model lives in one tab.

▶ Open Room Acoustics and RT60 Reverberation Time simulation

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