Re: Is there a limit to how loud a group of musicians can get?

Hi Marino,

That’s a very interesting question. I congratulate you in not only 
asking it but in continuing to write what’s really behind your asking. 
My initial thoughts were much different before reading the rest of your 
examples.

Let me start by defining a couple terms that we don’t want to confuse. 
First there is the total amount of sound energy that is being produced 
at the source. The second is the loudness we hear at some point in 
question. If we were to do an experiment, we might use speakers in 
place of flutes and a microphone as our ears. Instruments could 
record the sound energy being produced at the source as well as the 
amount of sound being heard at some other point. 

To answer the first part of your question, certainly millions of flutes 
would take lots of effort on the part of the people, as would electronic 
substitutes; and there is probably no limit to this. So let’s say that 
getting all the people in China playing would make a lot of noise. If 
the population of India were to join in, that would be still MORE noise.

Now, would it sound any louder to us? Two factors contribute to a 
limit in this regard. First there is the wave nature of sound. Each 
individual source makes its own set of waves to travel through the air. 
These waves are compression waves and are manifested as 
variations (slight increases and decreases) in normal air pressure. 
We hear loudness as the amount of this variation as it reaches our 
ears. However, since each wave is trying to raise and lower the 
pressure, there is always interference among multiple sources; and 
a million players would not sound that much louder. Even two 
sources could sound less at specific locations. This is a problem 
with stereo systems in a large room… there are places called nodal 
regions where the two speakers create destructive interference and 
listening to both speakers is less than either alone. The exact 
locations changes for each frequency played and is usually not a 
problem. But for the best overall sound, you should remain equally 
distant from each speaker. So lots of flutes may not seem louder 
than a few.

The other limiting factor is the need for the sound to follow the curve 
of the earth and not be absorbed by obstacles in the path. Lower 
frequencies will curve more than the high notes. You may have heard 
the low rumble of distant thunder compared to the sharp crack of a 
near strike. It’s the same event whether here or there; but we hear it 
differently due to the nature of sound wave propagation. Also just as 
carpet, drapes and furniture affect the sounds in our homes, the 
landscape will absorb much of the sound that does hug the ground.

Would people go deaf? Well, at Christmas, we have a local concert 
featuring >200 tubas on stage. Unless they’re already deaf, it doesn’t 
seem to bother them. Would 2,000 tubas be worse? I think the 
interference effect and their need to spread out serves as their 
protection. 

At what point would an outside audience not notice a louder concert? 
No personal experience with this; but let's pretend we start a 
kilometer away from center stage. I know we can hear the local high 
school band practice at that distance (mostly the drum section—why 
no flutes?). I’d guess that ten bands on the field would sound louder. 
If we wanted a thousand bands, we would need to expand the "stage 
area" a hundred fold. Now some of the bands would be getting 
closer and some would be farther away. For a million bands, my 
house would now be within the concert itself, and the interference 
effect would limit my hearing any increase in loudness. It might be 
easy to say that we’ve found the limit. But for someone living 10 km 
from the school, they would just be starting to hear the music and it 
would continue to get louder for a while as the bands grew to ten 
million. So, it seems that this answer doesn’t have an actual value, 
but is dependent on the location of the observer.