A woman stands a distance d from a loud motor that emits sound uniform.docx

A woman stands a distance d from a loud motor that emits sound uniformly in all directions. The sound intensity at her position is an uncomfortable 2.1×10-3 W/m2. At a distance 3.1 times as far from the motor, what are (a) the sound intensity and (b) the sound intensity level relative to the threshold of hearing?
Solution
1.
Intensity is given by
I = P/A = P/(4*pi*r^2)
Since Source is same at both distances, So
intensity is inversely proportional to square of distance r
I1/I2 = (r2/r1)^2
I2 = (r1/r2)^2*I1
I2 = (d/(3.1*d))^2*2.1*10^-3 = 2.1*10^-3/3.1^2
I2 = 2.18*10^-4 W/m^2
2.
Sound intensity level = 10*log (I/I0)
I0 = threshold intensity level = 10^-12 W/m^2
SL = 10*log (2.18*10^-4/(1*10^-12))
SL = 83.38 = 83.4 dB
Please Upvote.
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1. A woman stands a distance d from a loud motor that emits sound uniformly in all directions. The
sound intensity at her position is an uncomfortable 2.1×10-3 W/m2. At a distance 3.1 times as
far from the motor, what are (a) the sound intensity and (b) the sound intensity level relative to
the threshold of hearing?
Solution
1.
Intensity is given by
I = P/A = P/(4*pi*r^2)
Since Source is same at both distances, So
intensity is inversely proportional to square of distance r
I1/I2 = (r2/r1)^2
I2 = (r1/r2)^2*I1
I2 = (d/(3.1*d))^2*2.1*10^-3 = 2.1*10^-3/3.1^2
I2 = 2.18*10^-4 W/m^2
2.
Sound intensity level = 10*log (I/I0)
I0 = threshold intensity level = 10^-12 W/m^2
SL = 10*log (2.18*10^-4/(1*10^-12))
SL = 83.38 = 83.4 dB
Please Upvote.