What is the correct formula for calculating noise level in decibels?

[Drizzy]

Homework Statement

When the distance to a sound source is doubled, the noise level will be halved. Yes or no?

Homework Equations

L = 10 lg(I/10^-12) or L = 10 lg(I/l₀)

The Attempt at a Solution

my book used the first formula in another question and it used the second one in this problem. I know how to solve the problem but what I don't know is where 10^-12 comes from. Because in the text where my book tries to explain sound they only write the first formula but then when they gave an example of a problem they used the second formula. Which is the real one and when do I use them?

 

[kuruman]

The first formula is the same as the second with l₀=10^-12 W/m². That's the so called threshold of hearing
http://hyperphysics.phy-astr.gsu.edu/hbase/sound/intens.html#c3
Both are real and either one can be used to answer this particular question. For other questions, I would say you should probably use the first one if a specific value for l is given. Here it is not, and it doesn't matter that it's not.

 

[Drizzy]

If I and I₀ are given and I calculate the value of L, what is L giving me? Is it the noise level when the intensity is I or is it the noise level difference from when it goes from I₀ to I?

 

[kuruman]

It is the sound level in decibels relative to the threshold of hearing. If you read on the hyperphysics link, the threshold of pain is 130 dB. You can solve the equation for I with I₀ = 10^-12W/m² and L = 130 dB, to get I = 10 W/m².