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 70 dB. An object emitting a sound with an intensity level of 20dB. An object emitting a sound with an intensity of 1.0 times 10^-5 W/m^2. 100 buzzers each producing a sound with intensity level of 60 dB. An object emitting a sound with an intensity level of 90 dB.

Explanation / Answer

decibel level is defined as 10*log10(I/I0)

where I=intensity of sound

I0=10^(-12) W/m^2

for the two buzzers, each has intensity of 70 dB.

if intensity of sound is I, then 10*log10(I/I0)=70

==>I=I0*10^7

total intensity of two buzzers =2*I

in decibel level,10*log10(2*I/I0)=10*log10(2*10^7*I0/I0)=73.0103 dB

second object:

intensity level is 20 dB.

third object:

intensity=10^(-5) W/m^2

then in decibel level, 10*log10(10^(-5)/10^(-12))=70 dB

fourth object:

decibel level =60 dB

let intensity is I.
then 10*log10(I/I0)=60

==>I=10^6*I0

intensity of 100 buzzers in decibel scale=10*log10(100*10^6*I0/I0)=80 dB

fifth object:

decibel level is 90 dB

so ranking will be :
fifth object > fourth object > first object > third object > second object

the blanks can be filled as below:

3
5
4
2
1

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