# ACOUSTICS - Reverberation Time

## Statistical Reverberation

As discussed in the Sound Behaviour topic on the Square One website, reverberation time (RT) is the simplest and most commonly used objective measure of the acoustic performance of a space. It is defined as the time taken for the sound level of a steady source to drop by 60dB after it is abruptly turned off and is given as a value in seconds.

The RT is basically a ratio of the weighted sound absorption coefficients of materials within a space to its volume. The quickest method of calculation is simply to weight each material by its surface area - which is known as a statistical RT. This method takes no real account of the actual geometry of a space, just the materials within it and an overall form factor. However, it is usually a good predictor and is very widely used.

An alternate method is to actually trace many thousands of acoustic rays randomly sprayed within the space and then to weight each surface by the number of ray intersections. This method usually produces different results to the statistical method as it focusses on the more acoustically significant surfaces and ignores those the sound can't actually get to.

As is usual with these things, the performance of the real room is likely to be somewhere between these two extremes. In this tutorial we are going to look at both calculations and modify some materials within a space. It is assumed here that you have already been through at least the introductory tutorials and are reasonably familar with the ECOTECT interface.

1. First open the  ReverberationTime.eco  model from the Tutorial Files folder located in your main ECOTECT Install directory.

The zone we are interested in here is called MainSpace. You will notice that it is a thermally complete zone, meaning that its envelope is entirely defined and that planes or surfaces do not project outside the space in any way.

This zone represents a small lecture room with concrete walls, a partially exposed concrete ceiling and a timber-clad concrete floor slab. The only real absorption in the room comes from a plywood panel bulkhead running the length of the room.
2. Now select the Statistical Reverberation... item in the Calculate menu.

This will prompt you to calculate interzonal adjacencies. This is a necessary step as it allows ECOTECT to pre-process your model, checking plane equations, surface areas and looking for adjacencies between zones. The prompt should look like the following:

Usually this calculation is very quick, however it is the overshadowing analysis that really takes the time. As we are not going to use this model for thermal analysis yet, we can simply turn off shading calculations.
3. Click the Settings... button in the prompt.

This will display the Inter-zonal adjacencies dialog box. We basically need to select the None option in the Overshadowing Accuracy selector, as shown below.

4. After selecting None, click the OK button.

This will display the Graphical Results dialog box. You will notice from the settings section immediately below graph that the volume of the zone has been already calculated at 333.6m³ and that it has been assigned 35 cloth-covered seats, which are currently 80% occupied.

From this information, recommended reverberation times for speech and music can be derived. This is shown as a faint blue band running the full width of the graph.

The RT graph of the MainSpace shows values for each of the 9 octave bands that represent the Ear's hearing range. The coloured lines represent three different equations for performing the statistical calculation, denoted as Sabine, Millington-Sette and Norris-Eyring (see the Sound Behaviour topic for more details). The bold line, in this case the blue Sabine, represents the equation whose results will be stored within the zone's RT array.

You will notice that the RT for speech frequencies (500Hz - 4kHz) are well above that recomended for speech, being closer to the upper limit recommended for music. The longer RT values are also biased towards the lower frequencies. Sound recording engineers would refer to such a room as 'boomy' or having a lot of 'bottom end'. This in itself may not be a problem as speech does not contain too many low frequencies, however recorded material such as a video may have, so we should really know how often such material may be used before we can assess it as a problem.

However, at speech frequencies the recommended RT for speech is around 0.7-0.8sec whereas the room currently has an RT at these freqencies of 1.2-1.4 sec, almost double.

We can adjust the RT of any space by simply changing the materials assigned to any of its surfaces. As an obvious first experiment, we are going to play with the material assigned to the area of dropped ceiling running through the centre of the room.

1. Click inside the main application window and then select the three objects indicated in red below.

You will note that they are currently assigned the PlywoodPanel material. To compare, we are going to assign them as SuspendedAbsorber and see what changes that makes to the RT graph.
2. Once the three objects are selected, click on the SuspendedAbsorber material in the Material Assignments panel and then click the Apply button at the bottom of the panel.

These are two quite different materials. The PlywoodPanel is relatively rigid but without significant mass. Thus it allows low frequencies to pass pretty much straight through creating an enclosed space within the ceiling that acts like a bass trap. Mid-to-high frequencies are reflected back into the space with relatively little absorption. The SuspendedAbsorber material on the other hand contains thick fibrous material with significant mid-high frequency absorption, as shown in the comparative animation immediately below.

You can view these graphs by double-clicking on the material in the Material Assignments panel to display the Element Properties dialog, and then choosing the Acoustic Data tab.
3. Next return to the Graphical Results dialog and click the Recalculate button.

This should display the following graph.

As you can see, this has significantly reduced the RT in the mid frequencies, basically the speech band - perhaps a little too much as it is now a little below the recommended RT for a space with that volume. Unfortunately, acoustic design is never as cut and dried as this. It may be that the potential occupiers of the space would prefer it a little 'dry'.

## Simple Exercise

As a simply exercsie, you should try to reduce the low frequency RT of the space. There are really very few materials that absorb low frequency sound. However, the ECOTECT Help File contains lists of the absorption coefficients of a wide range of different materials and absorbers. To access this list, simply open the Element Properties dialog and click the Help... button, or navigate within the help file to Modelling > Material Assignments > Material Data page.

You can add absorber to the space by either assigning it to an existing surface or by adding moveable partitions, which can be removed or adjucted to control the overall response.