You are standing in the middle of a large room listening to a cacaphony of sound

Question

You are standing in the middle of a large room listening to a cacaphony of sounds. Rank the intensity level of the sounds from each source (1=loudest, 2= next loudest, ...) Consider all objects to be right next to you. (Remember that if you have a tie, you skip some ranks.) If two values are within 0.1 dB from each other, consider them to be the same.
Ten buzzers each producing a sound with intensity level of 68dB.
One hundred buzzers each producing a sound with intensity level of 63dB.
Two buzzers each producing a sound with intensity level of 78dB.
An object emitting a sound with an intensity of 80dB.

Explanation / Answer

For the 10 buzzers...

Start with B = 10logI/Io for each Intensity...

68 = 10log(I/1 X 10-12)

I = 6.309 X 10-6 W/m2

So 10 buzzers have an intensity of 6.309 X 10-5 W/m2

B = 10log(6.309 X 10-5)/(1 X 10-12)

B = 78 dB

We have to do the same for the 100 buzzers

63 = 10log(I/1 X 10-12)

I = 1.995 X 10-6 W/m2

So 100 buzzers have an intensity of 100 times that which is 1.995 X 10-4 W/m2

B = 10log(1.995 X 10-4)/(1 X 10-12)

B = 83 dB

We have to do the same for the two buzzers

78 = 10log(I/1 X 10-12)

I = 6.309 X 10-5 W/m2

So 2 buzzers have an intensity of twice that which is 1.262 X 10-4 W/m2

B = 10log(1.262 X 10-4)/(1 X 10-12)

B = 81 dB

Thus the order is

One hundered buzzers at a total of 83 dB = Loudest

Next is two buzzers at 81 dB

Next is the object at 80 dB

Then the 10 buzzers at 78 dB

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