A guy is placed some distance away from 4 really loud plane engines and receives a loudness of 120 dB. what's the loudness that the guy would hear if 3 of the engines were turned off?

Question

anonymous · Answer

does sound level intensity add up? does this mean each engine was 30 dB?

shane_b · Answer

I'm surprised no one has answered this already.  At any rate, it's not simply additive.

If I'm not mistaken (it's been a while) the formula would be:
$$ΔdB_{avg}=10log(\frac{P_1}{P_2})dB$$Let P1 be the intensity of 1 engine and P2 be the intensity of 4 engines:
$$ΔdB_{avg}=10log(\frac{1}{4})dB=−6dB$$So the final value would be $$120dB+(-6dB)=114dB$$
If you think about it, that answer actually makes a lot more sense.  If you were standing next to 4 running jet engines and 3 of them were turned off, you wouldn't expect the noise level to go down to a whisper (30dB).  You're still standing next to a running jet engine :)

anonymous · Answer

Thanks! I ended up figuring it out haha. I appreciate the answer though. Unfortunately the Physics section on OS isn't as active as the Math one :/