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A sound level problem.

In my high school physics class the other day the teacher botched an example problem involving sound level (decibels).

1. Homework Statement
A single sound source produces 105 dB at a distance of 5.0 m. How far away must the observer be to not hear this sound at all?


2. Homework Equations
beta.jpg



3. The Attempt at a Solution
The reference intensity I0 is the lowest intensity a human can hear, 1 x 10-12 W/m2, so when the source is far enough away its intensity will be equal to this. The intensity of a sound falls off as 1/d2, so after substituting the information in the problem the equation above can be rewritten as follows:
sub.jpg

In this equation, d0 represents the distance to the sound source that produces the reference intensity and d is the distance to the original source, 5.0 m for this problem.
When this is solved for d0, the result is 177828d, or about 890 km. This can't be right! What happened? Thanks in advance for your help.
 

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