How far can your voice carry at 40 dB?

AI Thread Summary
To determine the lowest decibel level needed for a shout to be heard at 100 meters, the discussion centers on the formula β = 10log(I/Io) and the intensity equation I = P/A = P/4∏r^2. The correct answer is identified as 40 dB, but participants express confusion about how to apply these formulas without a baseline for comparison. There is speculation that the ability to discern a sound change of 1 dB may be relevant to the calculation. The suggestion is made to work backwards from the 1 dB threshold to find the corresponding radius for 40 dB. Understanding these concepts is essential for solving the problem effectively.
Kavorka
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You are in a park when you spot your friend 100 m away. At what lowest decibel should you shout your greetings so that your friend can just hear you? Assume that your friend has normal hearing.

My prof never gave an example of how to do this and I can't figure it out. The correct answer is 40 dB. We know that β = 10log(I/Io) and I = P/A = P/4∏r^2

I really just have no idea how to do this because they gave no baseline to compare the 100 m distance to.
 
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It might hinge on a person's ability to just barely discern a change in sound of 1dB. But that still won't get me to a solution.

Maybe try working backwards. If it's 1dB at 100m radius, at what radius is it 40dB?
 

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