Decibel question - how much increase per speaker?

Question

Can anyone tell me the relationship between the number of speakers (or other sources of sound) and the sound level.

For example, if you had a speaker playing at max volume and recorded the volume at 70db, then played another identical speaker next to it at max volume. What would the increase in total decibels be?

(Sorry i'm not sure how to explain this question properly, but i basically want to relate it to people in the audience at a rock concert - basically to define how 60,000 people shouting at the same level sounds just a bit louder than 1 or 2 people shouting!!).

Answer 1

If you had N speakers, all perfectly in phase and equidistant to your head, the sound intensity would scale as N. Double the number of speakers, double the sound intensity.

However, humans do not perceive sound in a linear way. When you double the sound intensity, we do not perceive it to be twice as loud. We perceive sound on a logarithmic scale We represent this using the decibel scale:

dB = 10*log[W]
which means "10 times the base 10 logarithm of the sound intensity (in watts/square meter)"

So, doubling the sound intensity leads to a decibel increase of only
10*log(2)
= 10*0.301
= 3.01 decibels

Now, when 60,000 people shout in a concert, the sound intensity from each of them decreases with the square of their distance to you. So, the furthermost people barely contribute at all. Even if they manage to generate 10 times the sound intensity (measured at your head) of a single person, you would still only perceive this to be a 10 decibel increase.

Answer 2

Remember, the decibel scale is logorithmic. Two 70db sound sources only equal 73db combined sound.
To quote someone else"
"Because decibels are logarithmic units and can't be added like other numbers, total combined output is not easily determined. As an example of anticipated data, if you were combining a 50 decibel level to another 50 decibel level, the result would be about 53 decibels rather than a total of the two. The greater the deviance between the two levels, the smaller the amplification addition. In certain cases, a really wide deviance can actually cause attenuation rather than amplification. Also, temperature and surrounding conditions, natural and man-made, all have an effect on the total sound output."

Answer 3

The reason why in large groups of people, it's not incredibly loud is because of destructive interference occuring between all the sound waves.

Consider a busy harbour with many boats moving around. One boat creates waves. And with more boats there will be more disturbance (the higher waves are comparable to the louder noises). However when you have many many boats the waves don't get any bigger because they are all going in different directions. The waves interact with each other and can cancel each other out. If it were the case where the wake of the boats were all created in the same direction at the exact same time, then they would amplify each other and then you would get your tidal wave or your loud noise.

Back to your speaker question. The problem with multiple speakers is that sound sort of expands from its origin. Imagine a speaker with concentric circles around it. Those are the sound waves.

If a second speaker with concentric circles is placed next to it, then where you see the circles overlapping will be louder and the places where the circles cross empty space will actually be quieter because two different parts of the waves are colliding.

I hope that makes more sense.

Answer 4

It's more complicated than you might think.

Decibels are a measure of sound pressure. We perceive sound pressure on a logarithmic scale. In other words, if sound is twice as strong we hear it as just a little louder. Twice as strong again and it's still just a little louder. Between the softest sound we can hear and the loudest is a difference of thousands of times! In decibels, 10 decibels is about twice as loud, but about ten times as much power.

If one person is talking in a room, thats; a certain level of sound on your ears. If two people are talking, that's not much higher, in fact not as much of a difference as to be noticeable. Also distance is important. A person ten feet away is half as loud as a person five feet away. A person two and a half feet away is twice as loud as five feet away!

If many, many people are shouting, some are close, some farther away. The waves caused by their voices are all out of phase so sometimes they strengthen each other and sometimes they cancel each other out. The room is very big so you don't get much of echoes and reflections off the walls, and human bodies are soft so they absorb reflections (ever notice how different a big room sounds when it's empty as when it's full of people?)

So one person shouting in your ear is much more sound than 80,000 people shouting in a large room!

Answer 5

db=10log60000=45 db

Answer 6

+db=10*log(p2/p1)
3 db=10*(log(2))
3 db=10*(.30103) twice the power
--------------------------------------------
+db=10*log(p2/p1)
+db=10*log(1000/1)
30 db= twice the sound level

deduction :
from 1 watt to 1000 watts is twice as loud