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.

An object emitting a sound with an intensity level of 100 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 1.0×10-5 W/m2.
100 buzzers each producing a sound with intensity level of 70 dB.

Explanation / Answer

First we have to understand that the net intensity of n times louder is given by
10 Log10(n) dB louder.
NOw,
(1) an object is emitting the sound of intensity level of 100 dB
Hence its net intensity will be = 100 dB
(2) Since it is also one object therefore ite net intensity of sound will be 80 dB.
(3) Two buzzers are producing sound of 90 dB.
So net intensity will be = 90 + 10Log10(2) = 93 dB
(4) Intensity in dB
I(dB) = 10Log10(I/Io) = 10 Log10(10-5/10-12) = 70 dB
(5)100 buzzers producing intesity of 70 dB
so net intensity will be = 70 + 10Log10(100) = 90 dB
Now the ranking will be
1,3,5,2,4

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