8.3 Reverberation time and room acoustics

Fundamentals of Reverberation Time

Reverberation time (RT) measures how long sound lingers in a space after the source stops. It directly shapes whether a room sounds clear enough for speech or rich enough for music, making it one of the most important metrics in room acoustics design.

Definition of Reverberation Time

RT60 is the standard measure: the time (in seconds) it takes for sound to decay by 60 dB after the source cuts off. A room with a long RT60 sounds "live" and echoey, while a short RT60 sounds "dead" and dry.

• RT quantifies sound decay duration and affects speech intelligibility, musical warmth, and overall acoustic quality in spaces like concert halls, classrooms, and studios.
• Early decay time (EDT) is an alternative measure that focuses on just the first 10 dB of decay, then multiplies that time by 6 to estimate a full 60 dB decay. EDT often correlates better with how listeners perceive reverberance, because our ears are most sensitive to the early part of the decay.

Calculation of Reverberation Time

Two main formulas are used to predict RT, and choosing the right one depends on how absorptive the room is.

Sabine equation:

$RT = \frac{0.161 \cdot V}{A + 4mV}$

• $V$ = room volume in $m^3$
• $A$ = total absorption in sabins (sum of each surface's area times its absorption coefficient)
• $m$ = air absorption coefficient (matters mainly at high frequencies in large rooms)

The Sabine formula assumes a diffuse sound field with relatively low, uniform absorption. It works well for live rooms where average absorption coefficients are below about 0.3.

Eyring equation:

$RT = \frac{0.161 \cdot V}{-S \cdot \ln(1 - \bar{\alpha}) + 4mV}$

• $S$ = total surface area in $m^2$
• $\bar{\alpha}$ = average absorption coefficient across all surfaces

The Eyring formula is more accurate when absorption is higher or unevenly distributed. Notice that as $\bar{\alpha}$ approaches 1 (a nearly fully absorptive room), the Eyring equation correctly predicts RT approaching zero, while the Sabine equation does not. For lightly absorptive rooms, both formulas give similar results.

Factors and Design Considerations

Factors Influencing Reverberation Time

• Room volume has the strongest effect. Larger spaces hold more sound energy, so RT increases. Cathedrals can have RT60 values above 5 seconds; a small office might be under 0.5 seconds.
• Surface materials determine how much sound is absorbed at each reflection. Hard surfaces like concrete and glass reflect most sound energy, extending RT. Soft or porous materials like carpet, curtains, and acoustic panels absorb sound and shorten RT.
• Furniture and occupants add absorption. A packed audience can significantly reduce RT compared to an empty hall, which is why designers account for both occupied and unoccupied conditions.
• Air absorption becomes relevant at high frequencies (above roughly 2 kHz), especially in large volumes like stadiums or aircraft hangars. The $4mV$ term in both formulas captures this effect.
• Room shape influences how evenly sound distributes. Rectangular rooms with parallel walls can produce flutter echoes. Fan-shaped or irregularly shaped rooms scatter sound more effectively.
• Frequency dependence is often overlooked but critical. RT varies across frequency bands because materials absorb different frequencies at different rates. A room might sound "boomy" if low-frequency RT is much longer than mid and high-frequency RT.

Design for Optimal Reverberation

Different spaces need different RT values. Here are common targets:

Speech-oriented spaces need shorter RT so words don't blur together. Music-oriented spaces benefit from longer RT, which adds warmth and blends instrumental tones.

Design strategies to control RT:

1. Adjust room dimensions to set the baseline volume and, therefore, the starting RT.
2. Select surface materials with appropriate absorption coefficients. For example, adding acoustic ceiling tiles to a classroom can drop RT from 1.5 s to under 1.0 s.
3. Incorporate acoustic treatments such as absorptive panels to reduce RT or diffusers to scatter reflections without removing energy.
4. Address frequency balance. If a room sounds boomy, add low-frequency absorbers (bass traps). If it sounds harsh, target high-frequency absorption.
5. Use acoustic simulation software (such as ODEON or EASE) to model and optimize RT before construction, saving costly post-build corrections.

The goal is always a balance: enough reverberation to give a space a sense of life and envelopment, but not so much that clarity suffers.