# How to calculate the reverberation time RT60 given dimensions of a room?

I'm trying to estimate RT60 based on reverberant sound. In order to generate reverberant sound, I am required to give dimensions of a room so that RIR is generated and is convolved with clean sound.
While reading few papers, they had different room dimensions and RIRs ranging from 0.1s to 1.5s.This had me puzzled. Now I'm trying to find out if it is possible to get RIR from a particular room dimension (lets say 5ftx5ftx10ft) so that it gives a specific RT60 (say 0.3s)
Here is one paper for example: https://arxiv.org/pdf/2302.04932.pdf
Table 1 in the paper shows the different room dimensions and the ending of the following paragraph states:
''' We simulate 200 RIRs for each room, which results in a total of 200×3=600 RIRs. We convolve each of the RIRs with one signal from the TIMIT test set, resulting in a total of 600 signals. The T60s range from 0.5 s to 1 s. '''

So, my question is, is there a way to create an RIR for a particular room dimension so that it has a specific reverberation time?

• Try RIR Generator. It also has a python version. Jul 5 at 6:48
• Thanks for pointing that out. Here also, it seems that they have fixed room dimensions, source position, receiver position and reverb time. My question still remains as to how they can create an RIR with a fixed reverb time with these factors fixed as well. What are the other variables that can be altered to get an RIR like this? Not sure if I'm making myself clear Jul 5 at 8:57
• You may adjust the absorption coefficients of each reflection plane of the room to achieve desired T60. Have a look at Sabine's equation. Jul 5 at 10:11

The reverb time depends on the acoustic absorption in the room. At lower frequencies this is primarily determined by the wall material and construction and other objects in the room. At higher frequencies the air itself becomes significant as well.

A crude formula for estimating reverberation time is Sabine's Formula

$$T_{60} = \frac{24 \log(10)}{c} \frac{V}{\bar{\alpha}S}$$

where $$c$$ is the speed of sound, $$V$$ and $$S$$ are the volume and total surface area of the room, and $$\bar{\alpha}$$ the average absorptions coefficient given as

$$\bar{\alpha} = \frac{1}{S} \sum_{k=1}^N \alpha_k S_k$$

This assumes that the room is bounded by N walls that each have a surface $$S_k$$ and an individual absorption factor $$\alpha_k$$

In almost all rooms, the reverb time is a function of frequency and in most cases it's significantly higher at low frequencies than at high frequencies: partially because of air absorption and partially because most surface materials do absorb more at higher frequencies.

The easiest way to dial in a reverb time is to use a single absorption coefficient that's the same for all surfaces and independent of frequency. However, this doesn't match well with reality and RIR that are generated that way tend to sound very unnatural.

In fact, getting the values and spatial distribution and frequency dependence of the absorption coefficients correctly is a big part of creating natural sounding reverb simulations.

• So, please correct me if I'm wrong in my understanding, using these formulae one would fix T60 value with a fixed set of room dimensions. And then using the imaging method RIR can be generated for the room by fixing the source and receiver positions. Jul 6 at 11:37
• No, that's not correct. The T60 is a function of the geometry AND the materials of the walls. The image method must include a means of modelling absorptive reflections. Jul 6 at 18:10
• By Room Geometry you mean the room dimensions and shape, right? Material of the walls would determine the absorption of incident sound waves, right? Jul 7 at 10:27
• @MuraliKadambi: that's correct. Jul 7 at 19:24