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.)

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

2. Two buzzers each producing a sound with intensity level of 78dB.

3. Ten buzzers each producing a sound with intensity level of 72dB.

4. Four buzzers each producing a sound with intensity level of 71dB.

Explanation / Answer

For 1, the dB is 80

For 2, we need the intensity of 1, multiply by 2, and then refind the new dB

78 = 10log(I/1 X 10-12) I = 6.31 X 10-5

B = 10log(2)(6.31 X 10-5)/(1 X 10-12)

B = 81.01 dB

For 3)

72 = 10log(I/1 X 10-12) I = 1.58 X 10-5

B = 10log(10)(1.58 X 10-5)/(1 X 10-12)

B = 82.0 dB

For 4)

71 = 10log(I/1 X 10-12) I = 1.26 X 10-5

B = 10log(4)(1.26 X 10-5)/(1 X 10-12)

B = 77.02 dB

So the order is 3, 2, 1, 4 from loudest to softest

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