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

Note that in dB:

n times louder is 10 log (n) louder.

Ten times louder means 10 dB louder.

100 times louder is 20 db louder.

Thus,

First case: 68 dB + 10 dB = 78 dB

Second case: 63 dB + 20 dB = 83 dB

Third case: 78 dB + 10log(2) dB = 81 dB

Fourth case: 80 dB

Thus, the ranks are:

First case: 4

Second Case: 1

Third Case: 2

Fourth Case: 3

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