If two firecrackers produce a combined sound level of 85 dB when fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add intensities, not dBs.]
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This is Giancoli Answers with Mr. Dychko. The sound level in the first case with both firecrackers going off at the same time it's going to be 10 times logarithm of 2 times the intensity of 1 firecracker, on its own, divided by I naught. And so the intensity in the second case was just 1 firecracker will be 10 times logarithm of I over I naught. We can rewrite, I mean, sound level 1 where you have both firecrackers it has 10 log 2 plus 10 log I over I naught, using the power rule for logarithms. Sorry, the multiplication rule for logarithms. So, that means if you take the logarithm of a product you can write it as logarithm of the first thing plus logarithm of the second thing. So, the first thing is the 2 and the second thing is the I over I naught. And so we can rewrite this whole thing as 10 log 2 plus 10 log I over I naught. Now, 10 log I over I naught is sound level 2, sound level of a single firecracker. So, we rearrange this by taking this to the left side then switching the sides around. And we get the sound level for a single firecracker is both together minus 10 log 2. So, that's 85 decibels minus 10 log 2 and that's 82 decibels for the sound level of a single firecracker.
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