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 110 dB.

An object emitting a sound with an intensity level of 50 dB.

An object emitting a sound with an intensity of 1.0×10-9 W/m2.

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

Answer 1

The rankings are,
1) An object emitting a sound with an intensity level of 110 dB.
2) An object emitting a sound with an intensity level of 50 dB.
3) Two buzzers each producing a sound with intensity level of 40 dB.
4) 100 buzzers each producing a sound with intensity level of 20 dB.
5) An object emitting a sound with an intensity of 1.0×10-9 W/m2.

let I is the intensity of each buzzer,
beta1 = 10*log(2*I/Io)

= 10*log(U/Io) + 10*log(2)

= 40 + 10*log(2)

= 43 dB

beta2 = 110 dB
beta3 = 50 dB

sound intensity level of sound,
beat4 = 10*log(I/Io)

= 10*log(10^-9/10^-12)

= 30 dB

let I is the intensity of each buzzer.
beta5 = 10*log(100*I/Io)

= 10*log(I/Io) + 10*log(100)

= 20 + 20

= 40 dB

so,

the rankings are,
1) An object emitting a sound with an intensity level of 110 dB.
2) An object emitting a sound with an intensity level of 50 dB.
3) Two buzzers each producing a sound with intensity level of 40 dB.
4) 100 buzzers each producing a sound with intensity level of 20 dB.
5) An object emitting a sound with an intensity of 1.0×10-9 W/m2.