• I’m thinking that the answers have incorrect unit. Even the question asked for ‘times’ so the answers shouldn’t be shown in ‘dB’. 100 times is correct but not ‘100 dB”. It looks like an error with the practice test.

• So this is a ridiculous question! I'm sorry that it exists...

Three basic sound principles:

1. Doubling the subjective loudness of the sound source = add 10 dB
2. Doubling the intensity level (or power) of the sound source = add 3 dB.
3. 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 two-fold increase in sound intensity is actually 3 dB.

That's my take on it, hope that helps!

Thank you for the thorough explanation. I was thinking about the doubling= 10 dB myself. There are lots of WTF questions, so sometimes you just need to do your best, or take your best shot and move forward. Thanks again for your responses.

• Anton,

This question requires knowledge on summation of dB. The solution is as follows...
30dB = 10dB + 10logX
logX = 2
X = 100
Another way to put it, if one machine produces 10dB, it will take one hundred of the same machines to produce 30dB.

Josh

• Josh, thank you for the great explanation. I got all that now. I was not used to that method before. Thanks again.

• Anton,

You're welcome.

For your interest, this formula explains the below stated by Adelina earlier...

Doubling the intensity level (or power) of the sound source = add 3 dB.

Josh

• Josh,

Thank you so much for clarifying, it was bugging me. I checked your math calculating the opposite way using the IL equation for 100 machines @ 10dB and I got 30 dB.

A

• You can also technically solve it without using logarithms and you won't get exactly 100, but it will be close; +3 dB is an approximation.