(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Decibel level from source at 1.0 m is 60.0 dB

Find dB level at distance 2.0 m.

2. Relevant equations

dB = 10 log_{10}(I/I_{0}) <- this one I know but couldn't see an application.

Forgot to add that I_{0}is equal to 1.0 x 10^-12 W/m^2

dB = dB_{i}- 20 log_{10}(r_{2}/r_{1}), where r_{2}is the farther sound source and r_{1}is the closer one.

3. The attempt at a solution

I arrived at the correct answer of 54.0 dB by using the looked up formula. But I'd rather know how to derive that formula that relates the source distances myself. I tried for a while but am unable to do it. Anyone able to give me some insight on how to arrive at the second formula?

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# Deriving a formula for calculating dB based on distance

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