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 of the sounds from each source (1=loudest, 2= next loudest, ...) Consider all objects to be right next to you. If two values are within 0.1 dB from each other, consider them to be the same.

100 buzzers each producing a sound with intensity level of 70 dB.

An object emitting a sound with an intensity level of 80dB.

Two buzzers each producing a sound with intensity level of 90 dB.

An object emitting a sound with an intensity of 1.0×10-9 W/m2.

An object emitting a sound with an intensity level of 100 dB.

Explanation / Answer

100 buzzers each producing a sound with intensity level of 70 dB.

SL = 10 log ( I / 10^-12) = 70

I = 10^-5 W/m^2

there are 100 buzzers, so I_total = 100 x 10^-5 = 10^-3

now new SL = 10 log ( 10^-3 / 10^-12) = 90 db

thirs loudest = 3

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An object emitting a sound with an intensity level of 80dB.

SL = 80 db

forth loudest = 4
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Two buzzers each producing a sound with intensity level of 90 dB.

SL = 10 log(I /10^-12) = 90

I = 10^-3

for two buzzers, I = 2 x 10^-3

new SL = 10 log ( 2x10^-3 / 10^-12) = 93.01 dB

second loudest = 2
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An object emitting a sound with an intensity of 1.0×10-9 W/m2.

SL = 10 log (10^-9 / 10^-12) = 30 dB

5th loudest = 5
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An object emitting a sound with an intensity level of 100 dB

SL = 100 db

loudest =1

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