Reverberation

When you clap your hands inside a large cathedral, you hear the sound linger for several seconds after the clap has ended. This persistence of sound after the source has stopped is called reverberation. It occurs because sound waves bounce repeatedly off walls, ceilings, floors, and other surfaces inside an enclosed space. Each reflection returns some sound energy to the listener, so instead of hearing a single sharp clap, you hear a gradually fading wash of sound. Reverberation is distinct from a simple echo: an echo is a single, clearly distinguishable reflection, whereas reverberation is the cumulative effect of hundreds of overlapping reflections arriving in rapid succession. The amount of reverberation in a room depends on the room's volume and on how well its surfaces absorb sound. Hard, smooth surfaces such as stone, glass, and concrete reflect most of the sound energy they receive. Soft, porous materials such as curtains, carpet, and acoustic foam absorb energy, converting it into tiny amounts of heat through friction at the material's surface. Architects and acoustic engineers carefully balance these properties when designing concert halls, recording studios, and lecture theatres. Too little reverberation makes a space sound unnaturally 'dead'; too much causes speech to become unintelligible and music to blur into a muddy roar. Reverberation has a precise, measurable quantity: the reverberation time, symbol RT₆₀, defined as the time taken for the sound pressure level to fall by 60 decibels after the source stops. This corresponds to the sound intensity dropping to one-millionth of its original value. The value of RT₆₀ that is considered ideal varies with the intended use of a space — roughly 0.3–0.5 s for speech, 1.5–2.5 s for orchestral music, and up to 6 s or more for a pipe-organ recital in a cathedral.

Key takeaways

Sound Travels and Reflects
The Build-up and Decay of Energy
Sabine's Formula and Absorption
Practical Implications

Sound Travels and Reflects

A sound source emits pressure waves that spread outward at approximately 343 m/s in air at 20 °C. When a wave hits a surface it is partly reflected and partly absorbed. The reflected wave travels on to the next surface, where the process repeats. In a typical room a single sound event may undergo hundreds of reflections per second, each one slightly weaker than the last because some energy is lost at every surface.

The Build-up and Decay of Energy

While the sound source is active, energy continuously enters the room. At the same time energy is being lost to absorption. Eventually these two rates balance and a steady sound level is established — the room is said to be 'fully reverberant'. When the source is switched off, no new energy enters but absorption continues, so the sound level decays smoothly (approximately exponentially in an ideal room). The listener hears this as the characteristic dying tail of reverberation.

Sabine's Formula and Absorption

Wallace Clement Sabine discovered in 1900 that reverberation time depends on the room volume V and on the total sound absorption A of all surfaces. Each surface material is characterised by an absorption coefficient α (dimensionless, between 0 and 1): α = 0 means perfect reflection; α = 1 means perfect absorption. The total absorption is A = Σ(α × S), where S is the area of each surface. Sabine's empirical formula then predicts RT₆₀ directly from V and A.

Practical Implications

Adding more absorptive material (increasing A) shortens RT₆₀. Increasing the room volume V lengthens it. This is why a small, fully carpeted recording studio has a very short reverberation time, while an enormous stone cathedral — high volume, negligible absorption — can have RT₆₀ of 6–10 seconds. Engineers use adjustable acoustic panels, variable curtains, and even electronic artificial reverberation to tune RT₆₀ for different types of performance.

The Key Equation

RT_{60} = \frac{0.161 \, V}{A} = \frac{0.161 \, V}{\displaystyle\sum_{i} \alpha_i S_i}

RT_{60} — Reverberation time (s): Time for sound pressure level to decay by 60 dB after the source stops.
0.161 — Sabine's constant (s m⁻¹): An empirical constant derived from the speed of sound in air at room temperature (= 24 ln 10 / c ≈ 0.161 s m⁻¹ at 20 °C).
V — Room volume (m³): The total interior volume of the enclosure.
\alpha_i — Absorption coefficient of surface i (dimensionless (0–1)): Fraction of incident sound energy absorbed by surface i; 0 = perfect reflector, 1 = perfect absorber.
S_i — Area of surface i (m²): Surface area of the i-th panel or material zone inside the room.
A — Total acoustic absorption (m² (sabins)): Sum of αᵢSᵢ over all surfaces; sometimes called the 'equivalent absorbing area'.

Worked Example

Problem. A rectangular lecture theatre has dimensions 15 m × 10 m × 4 m (length × width × height). The total surface area of the room is 620 m². The average absorption coefficient of all surfaces combined is 0.12. Calculate the reverberation time and comment on its suitability for speech.

RT_{60} = \frac{0.161 \times 600}{74.4} \approx 1.30 \text{ s}

Answer. The reverberation time is approximately 1.30 s. This is longer than the recommended 0.3–0.5 s for clear speech intelligibility. The architect should increase acoustic absorption — for example by adding carpet (α ≈ 0.35), upholstered seats (α ≈ 0.55), or acoustic ceiling tiles (α ≈ 0.70) — to bring RT₆₀ below 0.6 s.

Figure

Diagram

Origins · 1 minWallace Clement Sabine and how this was discovered

Wallace Clement Sabine

1868–1919 · American

Sabine is regarded as the founder of architectural acoustics. Working at Harvard University around 1895–1900, he conducted meticulous experiments in the university's Fogg Art Museum lecture hall, dragging seat cushions in at night to systematically vary the absorption and measuring reverberation times with a stopwatch and his own ears. From this data he derived the empirical formula RT₆₀ = 0.161 V / A, transforming what had been guesswork into a precise engineering science. He applied his formula to the design of Boston Symphony Hall (1900), still regarded as one of the finest concert halls in the world. Sabine could not afford proper measuring instruments, so he used a pipe organ, a stopwatch, and his remarkably trained musical ear to detect when a tone had faded below audibility — carrying out thousands of measurements by himself, mostly between midnight and 5 a.m. to avoid background noise.

Sound Reflection and Echoes — Reverberation is the cumulative result of many sound reflections; understanding single reflections and echoes is the essential prerequisite.
Sound Wave Properties — Reverberation times and decibel decay only make sense once you understand frequency, amplitude, and intensity of sound waves.
Sound Absorption and Acoustic Materials — The absorption coefficient α is the central material property in Sabine's formula, directly controlling reverberation time.
The Decibel Scale — RT₆₀ is defined as a 60 dB drop in sound pressure level; a solid grasp of the logarithmic decibel scale is required to interpret this definition.