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.
1 2 3 4 5  An object emitting a sound with an intensity level of 50 dB.
1 2 3 4 5  An object emitting a sound with an intensity of 1.0×10-5 W/m2.
1 2 3 4 5  Two buzzers each producing a sound with intensity level of 40 dB.
1 2 3 4 5  100 buzzers each producing a sound with intensity level of 20 dB.
1 2 3 4 5  An object emitting a sound with an intensity level of 110 dB.

Explanation / Answer

Intensity is directly proportional to sound in dB

For an object emitting a sound with an intensity of 1.0×10-5 W/m2:

sound level in dB = 10*log(1*10^-5/(1*10^-12))

= 70 dB

Now for Two buzzers each producing a sound with intensity level of 40 dB.

So, total sound intensity,I = 10^4*1*10^-12 = 1*10^-8 W/m2

So, sound intensity of each buzzer = 1*10^-8/2 = 5*10^-9

So, sound intensity of each in dB = 10*log(5*10^-9/(1*10^-12)) = 37 dB

Similarly for 100 buzzers each producing a sound with intensity level of 20 dB.

sound intensity of each = 10^2*10^-12/100 = 1*10^-12 dB

So, in dB = 10*log(1*10^-12/(1*10^-12)) = 0 dB

So, the ranking is

1 --> e (110dB)

2 --> b(sound intensity of 1*10^-5 W/m2)

3 --> a

4 --> c

5 --> d

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