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.

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

An object emitting a sound with an intensity level of 10dB.

An object emitting a sound with an intensity of 1.0×10-5 W/m2. An object emitting a sound with an intensity level of 50 dB.

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

Explanation / Answer

Two Buzzers:

sound Level = 10 log(I / 10^-12)

40 = 10 log(I / 10^-12)

I = 1 x 10^-8 W/m^2

Inet = 2 I = 2 x 10^-8

sound level = 10 log(2 x 10^-8 / 10^-12) = 43 dB

2nd Case: AN object with intensity of 10 dB .

3rd Case: I1 = 1 x 10^-5 W/m^2

50 = 10 log(I2 / 10^-12)

I2 = 1 x 10^-7 W/m^2

Inet = I1 + I2 = 1.01 x 10^-5 W/m^2

sound level = 10 log(1.01 x 10^-5 / 10^-12) = 70.04 dB

4th case:

20 = 10 log( I / 10^-12)

I = 10^-10

Inet = 100I = 10^-8

Sound level = 10 log(10^-8 / 10^-12) = 40 db

3rd case > 1st case > 4th case > 2nd case

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