What do COVID-19 and acoustic feedback have in common?

While we're locked down, we can only imagine the sound of acoustic feedback resonating throughout a concert venue. But what connection does it have with the COVID-19 virus?

At the time of writing we're locked down at home in the UK. Every day there is a government briefing on TV telling us what they are doing, what we should be doing, and how this damned thing is eventually - maybe - going to end.

As you are probably well aware, people who are experts, or think they are experts, sometimes talk down to the public. They believe that because the general public has little knowledge of their specialist subject then they are incapable of understanding it even if explained clearly.

But here in the UK, the advice from the government's experts (by which I most definitely do not mean everyone who thinks they are an expert, looking at you Piers Morgan) has been mostly well-presented.

One point in particular has been their explanation of the R0, or basic reproduction number, of the virus. I'm not an expert by the way, I'm listening to the experts and I'm repeating what they say, hopefully accurately.

R0 represents the number of people a person who has the virus can be expected to infect. So if a virus, in combination with its environment and other factors, has an R0 of 2, then if you're infected you will infect two more people before you recover. They will infect four people, then eight, then sixteen. Ten rounds of that and more than a thousand people are infected. Sixteen rounds of that and its 65,536, which coincidentally is the number of bits used in 16-bit digital audio (another connection!).

Even an R0 of 1.1 is bad enough. Ten rounds and nearly three times as many are stricken.

So what's the magic R0 number?

The answer is 1. One infected person will infect one more, then one more again, then one more again, as each in turn recovers and becomes immune. The virus retains its hold on the population, but doesn't get any worse.

This gives us the clue. If the R0 can be less than one then the number of infections goes down. If it is, say, 0.5, then if 1024 people are infected, they pass the virus on to 512, then 256, then 128, then 64, then 32, then... after ten rounds only one person is infected, and it's a mere 1 in 2 chance that they will infect someone else.

Great. We now understand R0 and how viruses propagate. What does that have to do with acoustic feedback?

Acoustic feedback - R0 and loop gain

We all know acoustic feedback in live sound. It's that 'woooo' noise that happens from time to time when the engineer has been a little too optimistic about how loud they can go (hint - live sound isn't always about being loud.)

Let's trace the chain of acoustic infection...

Start with the singer making their best noises into the microphone. The microphone converts acoustic energy into electricity, it's amplified by the preamp, controlled by the channel fader and master fader, amplified by the power amplifier, then turned back into sound by the loudspeakers.

But...

Then the sound from the loudspeakers is picked up again by the microphone, turned into electricity, etc. etc...

So we have a complete circle, or loop as audio engineers like to call it. Sound goes round the loop over and over again.

This always happens. The sound from the loudspeakers is always picked up again by the microphone. However they are positioned, reverberation in the venue will see to that.

But we don't always hear feedback. Why is this so?

The answer is in the loop gain.

Like R0, the magic number is 1. This is the multiplication factor, or gain, around the entire loop.

There is a gain in the preamp and another gain in the power amplifier. But there are losses - in the conversion of sound to electricity in the microphone, in the channel fader, in the master fader, and in the distance between the loudspeakers and the microphone (or their relative positioning and directivity of the mic). There's also a loss in the absorption of the room, but this can be large or small depending on how reverberant the room is.

Taking all of these gains and losses into account we have the loop gain.

If the loop gain is greater than one, then each time the signal goes round the loop it will get higher in level, higher and higher, and 'woooooo' you have feedback.

If the loop gain is less than one, each time the signal goes round the loop it becomes more and more attenuated and eventually dies out to below the noise level.

It isn't a good thing to have a loop gain of just slightly less than one because you get 'ringing' which is an oscillation at what would have been the feedback frequency following each sound input into the microphone. It sounds bad - live sound engineers please don't tolerate it.

To be feedback-free and also free of ringing, the loop gain has to be well under 1. This is achieved by placing the microphone behind the loudspeakers; angling the setup so that the loudspeakers are in the null of the microphone's response; equalizing the system so that the gain at whatever would have been the feedback frequency is lower; and the engineer being in control of what's going on.

So where an R0 of slightly less than one is better than being greater than 1, ideally we would like an R0 well under 1. Same with acoustic feedback - the loop gain needs to be well under 1 so that there is neither feedback nor noticeable ringing.

So who'd have thought it? Sound engineering and viruses have something in common.

Stay home, stay safe, keep the loop gain well under one.