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## Homework Statement

A rock group is playing in a bar. Sound

emerging from the door spreads uniformly in

all directions. The intensity level of the music

is 116 dB at a distance of 5.77 m from the

door.

At what distance is the music just barely

audible to a person with a normal threshold

of hearing? Disregard absorption.

Answer in units of m.

So,

Given-

I1(dB) (the intensity level 5.77 meters from the door)=116 dB

r1 (distance from door when intensity is 116 dB)= 5.77 m

Io (Intensity at threshold of hearing)= 1e-12

Unknown-

r2 (Radius at threshold of hearing)

P (power of sound source)

I1(w/m^2) (intensity 5.77 meters from door in watts/meters squared)

## Homework Equations

dB=10log(I/Io)

P=4*I*π*r^2

r=√(P/4πI)

## The Attempt at a Solution

First, I changed the given Intensity into W/m^2 instead of hertz.

dB=10log(I1/Io)

116=10log(I1/1e-12)

11.6=log(I1/1e-12)

10^11.6=I1/1e-12

(1e-12)(10^11.6)=I1

.3981071706=I1

So that's the Intensity at the spot from the door mentioned, so now I calculated the power source.

P=4*I1*π*r1^2

P=4*.3981071706*π*5.77^2

P=166.5564633

So, now that I had the power source, I calculated the radius needed to achieve threshold of hearing

r2=√(P/4πIo)

r2=√(166.5564633/4*π*1e-12)

r2=√(166.5564633/1.256637061e-11)

r2=√1.325414222e13

r2=3640623.878

Doesn't seem right... 3.6 million miles seems overkill.

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