sound intensity and difference in dBs relationship question
I took a practice PP&D exam and got the following question that seems oddly worded and possibly think incorrect:
A sound of 30 dB is how many times more intense that a sound intensity of 10dB?
A) 10 dB
B) 100 dB
C) 20 dB
D) 50 dB
The correct response was B "Each increase of 10dB is a twofold increase in sound level intensity. There for two twofold increases would be 10x10 which equals 100."
This seems oddly worded and I don't really understand this. If 100 is correct, then wouldn't the correct response be 100 and not 100dB. the units shouldn't be there I don't think. I mean how could a 20dB difference be 100 dB louder? From what I've read each time it increases by 10dB it would essentially be 10 exponent 1, so 10dB to 20 dB would be 10 exponent 2= 10x10=100 times louder, then again at 30dB I think so it would be then 1000 times as loud? I'm not sure. Please review and advise. I appreciate the clarification.

So this is a ridiculous question! I'm sorry that it exists...
Three basic sound principles:
 Doubling the subjective loudness of the sound source = add 10 dB
 Doubling the intensity level (or power) of the sound source = add 3 dB.
 Doubling the distance from the sound source = subtract 6 dB.
Referenced from the book Mechanical and Electrical Equipment for Building (Acoustics, Chapter 17) & also explained a bit in various other books.
So yeah I agree, the question is bad. It's not clear at all whether they are asking about intensity (power / sound energy) or loudness (human perception). The difference between the two is that the human ear doesn't actually perceive a doubling in intensity (+ 3 dB) and what we perceive as "twice as loud" is actually an increase of 10 dB.
If we assume it's asking how many times louder is 30 dB than 10 dB it follows that 10 dB + (2 x 10 dB) = 30 dB; we double the sound twice, therefore the sound is 4 times louder to the ear. But then the answers don't make any sense whatsoever, and the question clarification is wrong because a twofold increase in sound intensity is actually 3 dB.
That's my take on it, hope that helps!
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