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 50 dB.

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

100 buzzers each producing a sound with intensity level of 20 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 80dB.

Explanation / Answer

here,

Intensity level, L = 10^(Db/10)*no of equipments ---------------(1)
Will be using above eqn for each case

Case 1:
dB = 50dB
n = 1

L1 = 10^(50/10)*1
L1 = 10^5

Case 2:
dB = 40dB
n = 2

L2 = 10^(40/10)*2
L2 = 2*10^20

Case 3:
dB = 20dB
n = 100

L3 = 10^(20/10)*100
L3 = 10^12

Case 4:
Sound intensity level is given as:
L = 10*log(I/Io)
L = 10*Log(10^-9/10^-12)
L = 30 dB

so,
L4 = 10^(30/10)*1
L4 = 10^3

Case 5 :
dB = 80dB
n = 1

L5 = 10^(80/10)*1
L5 = 10^8

Increasing order : L4 < L1 < L5 < L3 < L2

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