How much should volume change for an empty room vs one full of bodies?

So tonight I'm doing a film screening. The room is small and will have about 20 people in it. The room is already absorbent, with painted wood on the walls, carpet on the floor, acoustic tile drop ceiling. I have a volume setting that sounds right to me when the room has nobody else in it. But adjusting the volume during the screening won't really be possible without disruption, so I'm hoping to tweak it before hand.

Does anyone have a rule of thumb for how much to tweak volume levels based on the number of people in the room?

2 Answers

For a room that is already very absorbent simply adding people to the room is not going to make a noticeable difference. Consequently, you should balance the room like a normal mixing theatre would. The rule of thumb here is - for smaller rooms - Pink noise at 0dBU should give you approximately 80dBSPL/C/Slow (That's C-weighted with Slow integration) when played through each speaker (Left, then Right). I would not adjust it beyond these parameters. Most of the time, it's not possible to line up the room, but if you get a chance to do so, this is how you should do it. Depending on your system 0dBU reference is found at -20dBFS on your system metering.

On the other hand, if you had a very reverberant room, putting people in would significantly increase the sound absorption and would consequently reduce the Rt60 value. Even so, I would still not change the reproduction level beyond the above values.

Well, I believe what you are asking does not have a particular "one-number-fits-it-all" solution.

What could possibly be done (even to an approximate degree) is to somehow think of the difference when the room is empty against the room being occupied by people.

The only difference of course is the people. So the main difference they will introduce to the sound is the absorption, which mainly affects reverberation. Of course there will be "spatial masking" for people standing/sitting behind other people but this is something you cannot solve by tweaking one volume knob.

I will try to "solve" a problem here to find what is the influence of the people to the reverberation time. So if we assume (for simplicity) that Sabine's formula is valid for your room we know that

$\\&space;RT_{empty}&space;=&space;\frac{0.161&space;\cdot&space;V}{A_{empty}}&space;\\&space;\\\\&space;RT_{full}&space;=&space;\frac{0.161&space;\cdot&space;V}{A_{full}}$

So by subtracting one from the other to find the difference we have

$\\&space;RT_{empty}&space;-&space;RT_{full}&space;=&space;\frac{0.161&space;\cdot&space;V}{A_{empty}}&space;-\frac{0.161&space;\cdot&space;V}{A_{full}}&space;\implies&space;\\&space;\\\\&space;\implies&space;RT_{empty}&space;-&space;RT_{full}&space;=&space;\frac{(0.161&space;\cdot&space;V)&space;\cdot&space;(A_{full}&space;-&space;A_{empty})}{A_{empty}&space;\cdot&space;A_{full}}$

We know of course that

$A_{full}&space;=&space;A_{empty}&space;+&space;A_{people}$

and the absorption of the people can be found on some tables available online. So the total absorption of the people is this number (absorption for one person) times the amount of people. So, after some substitutions and manipulations we can find

$RT_{full}&space;-&space;RT_{empty}&space;=&space;\frac{0.161&space;\cdot&space;V}{A_{empty}}&space;\cdot&space;\frac{A_{people}}{A_{empty}&space;+&space;A_{people}}&space;=&space;RT_{empty}&space;\cdot&space;\frac{A_{people}}{A_{empty}&space;+&space;A_{people}}$

where here A for people is the total absorption of all the people (what you found on the table times the amount of people present). You can see that the difference is the initial reverberation time scaled by the percentage of the absorption introduced by the people over the total final absorption.

Finally assuming (as we have already done in our choice to use Sabine's formula) that the field is diffuse we can approximate a halve of reverberation time with a halve in the total energy, leading to a decrease of 6dB. As can be seen from the above formula in order to achieve such a huge decrease in "volume" (abuse of terminology here!) we would have to introduce absorption equal to 2/3rds of the empty room's. Which is quite too much to ask from 20 people (in my opinion).

Now, all this nonsensical "derivations" have a lot of conceptual flaws (obviously), so first of all please do NOT consider this a mathematical or physically rigorous approximation. Now, the flaws are:

1. The sound field is not diffuse.
2. The absorption is not well distributed.
3. The total absorption will be considerable.
4. The whole room is not excited due to speaker directivity, which of course is frequency dependent.
5. Possibly something else I can't think of at the moment.

Now, 1, 2 and 3 render Sabine's formula "not-so-useful". 1, also makes our assumption that halving the reverberation will halve the energy in some places in the room, incorrect.

With all those mentioned we can conclude that our estimate (whatever this will be), if based on what we did up to this point will be an overestimate (by a good amount) of the resulting reduction. So, as I said above, looking for a 6dB reduction even with this overestimated derivation is too much, even more when adding the fact that we have overestimated by a good amount.

To conclude this too lengthy answer (I strongly apologize for that, I just wanted to make my way of thinking as clear as possible to avoid misunderstandings) I believe that an increase of a couple of dBs will be quite enough (if even needed).

Phew..., done!

• Trying to be gentle as you're a new contributor, but I don't think I can sleep without making a few points here. Firstly, you're listing a whole bunch of equations and doing a whole bunch of calculations that are not actually related to the original question, then concluding that those equations weren't that useful anyway and then coming up with some assumed numbers off the top of your head. I think if you're going to take a scientific approach to this, it needs a little more rigour or just a 'rule of thumb' which was the original question in the first place. HTH. – Mark May 24 '19 at 11:48
• Thanks @Mark. Point taken and as I said, I just used the calculations just to show my way of thinking/"reasoning" and then tried to make clear that this was just an approximate path (this is why I didn't bother use any numbers to calculate any value). I didn't really intend to follow a "scientific" path from the beginning. I guess you are right about it though. Thanks again :). – ZaellixA May 24 '19 at 12:07