Single-Number Metrics

Figure 1. Two very different sounds with identical dBA values.

In acoustics and audio, we need to quantify the performance of rooms and systems, and sound in general. To do this, we employ a series of metrics ranging from Reverberation Time, Speech Transmission Index and Sound Pressure Level (dB SPL), to name but a few. Yet, although all of these measures are spectrally and spatially dependent, this is often forgotten or, in some cases, not even realized.

Take for example, the quantification of the amplitude or perceived loudness of a sound. Here, by far the most common measure is the A-weighted SPL, or dBA level. It is a quick and convenient way of describing the level of a sound. We all know that 95dBA, for example, is pretty loud and potentially dangerous if exposure is prolonged, whereas 55dBA to 60dBA would be a typical mid-level sound, approximating normal speech. And 30dBA to 35dBA would be considered to be fairly quiet, although not if this were the background noise level in a concert hall, where the level should, perhaps, only be 20dBA to 25dBA or less.

So, with many of these measures, there is also a contextual element. A reverberation time of two seconds might be appropriate for a concert hall or traditional church, but too short for a large cathedral and way too long for a movie theater or classroom. By using a single-number descriptor, we can get a feel for the acoustic environment or situation. A Speech Transmission Index value of 0.50, say, may be appropriate for a basic paging system, but would be a disaster if this were the measured intelligibility in a drama theater or lecture hall.

Figure 1 shows the 1/1 octave band spectra of two steady-state sounds. As the figure shows, the sounds are quite different, with one (S3) being predominantly “hissy” (red bars), while the other (S2) sounds more like a roar or a rumble (blue bars). Thus, not only do their spectra look different, but the two also sound very different, and S3 sounds louder than S2…yet they both measure exactly 70dBA. In other words, according to our most widely used and adopted measure of sound level that is supposed to describe the human response to sound, they are the same!

Now, it is well known that using dBA as a measure of loudness or perception is flawed, but we still use it all the time because we need to create a single number that we can understand. To help see the differences between the two sounds a little more clearly, in Figure 2, I have plotted the envelope curve for the two spectra. It is immediately apparent how different the two sounds are here.

Figure 2. The sound spectra of Figure 1 replotted as an envelope function.
Figure 2. The sound spectra of Figure 1 replotted as an envelope function.

However, dBA is not the only way of measuring or quantifying the amplitude of a sound. For example, applying a Noise Criteria (NC) measure immediately shows the sounds to be quite different with values of NC60 and NC75 being obtained. There are, of course, several other different measures that could be employed, but the point is that single-value metrics can be misleading and throw away a lot of useful information.

Reverberation Time is another parameter that I use every day, and I am as guilty as everyone else of trying to compress the function into a single value. Traditionally, if quoting a single RT figure, the 500Hz octave band value was (and still is) used. However, Reverberation Time can be (and normally is) highly frequency dependent. Take, for example, the RT characteristics shown in Figure 3, taken from three very different venues. All three curves measure 2.5 seconds at 500Hz, but these rooms sound radically different, as do the sound systems in them (pre EQ).

Currently, a common way to ascribe a single-figure RT value is to quote the Tmf, which is the average of the 500Hz, 1kHz and 2kHz bands. This makes no sense to me because the often longer 500Hz value is reduced in the averaging process, as the higher frequencies generally exhibit a lower RT. Not only that, but just by having the Tmf, you are left wondering what the averaging has done and immediately want to see the full curve! At least if you know you are dealing with 500Hz (the main power region of the voice and many musical instruments) you can get a feel for the situation.

Figure 3. Three Room Reverberation Time characteristics with same 500Hz value.
Figure 3. Three Room Reverberation Time characteristics with same 500Hz value.

But again, to really understand the situation, spectral analysis/data is required. The Tmf for the three rooms shown in Figure 3 is 2.4, 2.0 and 2.6 seconds, respectively. The tricky 2.5 seconds at 500Hz has been reduced to a rather more benign 2.0 seconds by the averaging process. This averaging method is not for me; I am sticking with the 500Hz octave band value. The longer RT values are still there to contend with; averaging them does not make them go away but, instead, masks their effect, leaving them lurking as a nasty surprise for the unwary!

Not only does reverberation time vary with frequency, but also generally with measurement position (particularly at low and mid frequencies), unless the room is highly reverberant and diffuse.

Figure 4 shows how the measured RT (T20) varied at 10 different points in a large reverberant space. The spread in results is less than for many other buildings I have measured, but the similarity in results at 2kHz and above is quite typical.

So, what is the take home from all of this? First: Don’t trust single-value indices, and second, know where (and how) the measurement was made. Now, I am off to check my bank account. On average, it is in the black, but apparently my bank doesn’t deal in averages. Rather, it charges me for every decline into the red (frequency also comes into that as well)!

Figure 4. Variation of reverberation time with measurement position in a reverberant space.
Figure 4. Variation of reverberation time with measurement position in a reverberant space.
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