Question 1191776: The intensity level of sound is measured on a logarithmic scale. The intensity level, β, of sound is defined in the following equation β=10 log I/Io where β is measured in decibels, and Io is the intensity of a reference level. The reference level is 1.0x10^-12 w/m^2
How much louder does a siren at 30 m away, with an intensity of 1.0x10^-2 w/m^2, sound compared to a whisper, which is 20 decibels?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the formula is B = 10 * log(I/Io)
B is the decibel level of the sound.
I is the intensity level of the sound.
Io is the intensity level of the reference.
the intensity level of the reference becomes:
Io = 1 * 10^-12 * w/m^2
w/m^2 equals watts per square meter.
when m = 30, the intensity level of the reference becomes:
Io = 1 * 10^-12 * w/900.
if the intensity level of the siren is equal to 1 * 10^-2 * w/m^2.
when m = 30, the intensity level of the siren is equal to 1 * 10^-2 * w/900.
I = 1 * 10^-2 * w/900.
the decibel level of the siren becomes:
B = 10 * log(1 * 10^-2 * w/900) / (1 * 10^-12 * w/900)
the 1 and the w/900 cancel out and the equation becomes:
B = 10 * log(10^-2/10^-12.
simplify to get:
B = 10 * log(10^10) = 100 db
the decibel level has increased by 100, since the decibel level of the reference signal is 0.
the intensity level of the signal has increased by a factor of 10^10.
this means that the intensity level of the siren is 10^10 times more than the intensity level of the reference level.
10^10 is equal to 10 billion, i believe.
the intensity level of the siren is 10 billion times the intensity level of the reference level.
you are given that the decibel level of a whisper is 20 db.
this is presumed to also be at a distance of 30 meters from the source of the whisper.
since the siren is 100 db and the whisper is 20 db, then the siren is 80 db higher than the whisper.
80 db = 10 * log(I/Io)
divide both sides of this equation by 10 to get:
8 = log(I/Io)
this is true if and only if I/Io = 10^8
10^8 is equal to 100 million.
this says that the sound of the siren has an intensity level that is 100 million times the intensity level of a whisper, given they are both the same distance from the listener.
that's what i think your solution is.
i think the rule of thumb is:
for each 10 db increase, the intensity level is increased by a factor of 10.
this means:
10 db increase = 10 * the intensity level.
20 db increase = 10^2 * the intensity level.
30 db increase = 10^3 * the intensity level.
....
80 db increase = 10^8 * the intensity level.
etc.
let me know if you have any questions.
i'll try to answer as best i can.
this is new to me, so take that into consideration.
theo
|
|
|
