A person standing a certain distance from an airplane with four equally noisy jet engines is experiencing a sound level of 140 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dBs.]
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This is Giancoli Answers with Mr. Dychko. The sound level for four aircraft engines together equals 10 times the logarithm of the total intensity of the 4 engines. So, that's 4 times the intensity of a single engine divided by some reference threshold appearing, I naught. And the sound level with what single engine will be 10 log of a single engine intensity divided by I naught. And we're going to use this rule for logarithms that says logarithm of have 2 things multiplied together is the logarithm of the first thing plus the logarithm of the second thing. And in this case we're going to say that the 4 is like the first thing the a and the b is going to be like the I over I naught, that's the second thing. So, we can read it as log of 4 plus log of I over I naught, and it's all getting multiplied by 10 and then distribute the 10 into the brackets and you have 10 log 4 plus 10 log I or I naught. And the reason this is useful is because it turns out that this part is the sound level for a single engine. So, we'll replace it with β1. And then we can rearrange this to solve for β1 bring this to the left side making it a minus and then switch the sides around. And we have sound level for 1 engine is sound level 4 engines minus 10 log 4. And that is 140 decibels minus 10 log 4 which is 134 decibels for a single engine.
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