- #1
JinM
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Homework Statement
A rock group is playing in a club. Sound emerging
outdoors from an open door spreads uniformly in
all directions. If the decibel level is 70 dB at a dis-
tance of1.0 m from the door,at what distance is the
music just barely audible to a person with a normal
threshold ofhearing? Disregard absorption.
Given:
dB1 = 70 dB
r1 = 1.0 m
Unknowns:
I1 = ?
r2 = ?
Io = 10^-12 W/m^2
dB1 is the decibel level at a distance of 1m from the door. r1 is distance from the door. I1 is intensity at a distance 1m (r1) from the door. Io is threshold of hearing, at a distance of r2 (unknown) from the door.
Homework Equations
dB = 10 log(I/Io)
I = P/A = P/4πr^2
The Attempt at a Solution
db = 10 log(I/Io)
70 = 10 log(I/Io)
7log10 = log(I/Io)
10^7 = I/Io
10^-12 * 10^7 = I
I1 = 10^-5 W/m^2 -> Intensity 1
I1 = P/A
10^-5 = P/(4π)
P = 1.3 x 10^-4 W
Now I used the same equation to find r of threshold of hearing:
Io = P/A
10^-12 = (1.3 x 10^-4)/(4πr^2)
r = sqrt([1.3x10^-4]/[10^-12x4π]) = 3216 m
This is what I got for r, but it just doesn't seem reasonable. Is this the correct answer? Have I done something wrong?
Thank you, and please do tell if my work is incomprehensible.