- 66

- 0

**1. 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.

**2. Homework Equations**

dB = 10 log(I/Io)

I = P/A = P/4πr^2

**3. 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.