Sound Decay: Where’s The Point? – Part 3

Part 1
Part 2
Figure 1. Family of RT curves for a large reverberant auditorium; note the lower times of the EDT curve.

“Sound decay” sounds like a disease that decrepit concert halls might suffer from, but that’s not what I mean. The time it takes for a sound to decay to inaudibility and the manner in which it does so are fundamental acoustic characteristics of a space. Indeed, for more than 70 years, they were the only objective measures and established design criteria to describe the acoustics of a space.

Sound decay, of course, is better known as “reverberation time.” This is a remarkably misunderstood acoustic parameter, considering its simplicity. The concept of reverberation time was conceived by Wallace Sabine in the mid-to-late 1890s after he had been set the task to improve the intelligibility of a notorious lecture room at Harvard (Fogg Art Museum). He discovered that, on average, around 60dB of sound decay in the room was audible, so a measure of reverberation time was proposed, as the time for a sound to decay by 60dB (i.e., to inaudibility). In the US, this is often erroneously termed RT60 (just consider the tautology of that for a start). Furthermore, reverberation time wasn’t proposed in terms of decibels originally, of course, because the dB wasn’t itself invented until more than 20 years later at Bell Labs!

There are several forms of reverberation time (i.e., subsets) and essentially two methods of measuring the parameter. ISO 3382 describes how reverberation time should be defined and measured. These days, due to its impracticality, we do not measure the room decay over the complete 60dB range. Instead, the decay time over either a 30dB or 20dB window is measured. These measures are then referred to by the descriptors T30 and T20 (not an RT60 in sight!).

Although simple in concept, the definition of reverberation time is, in fact, quite complex, being defined at one time as “the time, expressed in seconds, that would be required for the sound pressure level (SPL) to decrease by 60dB, at a rate of decay given by the linear least-squares regression of the measured decay curve from a level 5dB below the initial level to 35dB below.” This is termed T30.

A value for T, based on a decay rate over a smaller dynamic range (down to a minimum of 20dB extending from 5dB down to 25dB) is also permissible, provided the results are appropriately labeled T20. In practice, in most reverberant rooms, the values for T20 and T30 are similar, but the T30 measure is much more prone to corruption by background noise.

A slightly different definition of RT is “the duration required for the space-averaged sound-energy density in an enclosure to decrease by 60dB after the source emission has stopped.” From this definition, we can see that reverberation time may vary with measurement position in the room and a spatial average is therefore required to account for this.

In addition to the T30 and T20 measures, it is also possible to measure the T10 (i.e., the decay over a 10dB range), though in practice this is of limited use. The Early Decay Time (EDT) parameter, however, is very much more useful and is a measure of the sound decay over the first 10dB of a decay slope, without ignoring the first 5dB. EDT is spatially more dependent than T20 and T30, and is also highly dependent on the location and type of sound source employed.

Figure 2. Family of RT curves for a large reverberant space.
Figure 2. Family of RT curves for a large reverberant space.

So far, the frequency dependency of reverberation time has not been discussed, but RT can vary enormously with frequency. Figure 1, for example, shows a family of RT curves, measured in a large reverberant (unoccupied) auditorium. The T20 and T30 curves agree well with each other, but the EDT (red curve) is clearly quite different, being almost one second shorter at 1kHz. The frequency dependency of the reverberation time characteristic can be seen clearly. Figures 2 and 3 show two further, but very different RT characteristics, emphasizing the typical variations that occur in room reverberation.

As can be seen by the RT characteristic in Figure 2, the low frequencies take a much longer time to decay than the higher frequencies. Note also that, in this case, the EDT characteristic is similar to the other curves. Figure 3 shows another quite different RT characteristic.

Figure 3. T20 and T30 curves for a modern church (poorly balanced acoustic).
Figure 3. T20 and T30 curves for a modern church (poorly balanced acoustic).

ISO 3382 has now been split and extended into three different parts. Part 1, “Acoustics: Measurement of room acoustic parameters. Performance spaces,” is dated 2009 and describes a number of other room acoustic parameters apart from RT, such as Clarity and Envelopment. Part 2 (2008) is titled, “Acoustics: ‘Measurement of room acoustic parameters. Reverberation time in ordinary rooms.” Part 3 is titled, “Acoustics: Measurement of room acoustic parameters. Open plan offices.”

Reverberation time can be measured in two very different ways. In the first method, the room is excited to a steady state condition with a pink noise (or filtered pink noise) signal. When the sound source is switched off, the resulting decay time, over the period and frequencies of interest, is ascertained. Alternatively, the RT can be obtained by exciting the space with an impulse and measuring the resultant sound decay. The impulse can be a true impulse, such as that produced by a balloon burst or blank pistol shot, or a mathematically derived impulse from an exponential sine sweep (chirp) or Maximal Length Sequence, or via a two-channel transfer function measurement where pink noise or even program material can be used.

Each method has its pros and cons, which I will delve into next month. However, in the meantime, consider the range of reverberation times that can be encountered.

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