Sound Pressure Level Formula?

Question

Here is the deal, the SPL formula will tell me what dB a sound will be at once it reaches a certain distance, but I need something a little different. The SPL forumla is:

(SPL2 = SPL1 + 20log[d1/d2]) where 'd'=distance

Well, I need to know how to manipulate this formula so that it will tell me the DISTANCE at which a sound reaches a certain dB.

For example, let's say I have the original distance that the sound was measured at, for our purposes we will say that it was 90 dB at a distance of 20 feet. Without a bunch of trial and error, how can I tell what distance the sound will be 20 dB at?

Thank you!

By the way, I am not trying to cheat on homework or anything like that. I am not a physicist, nor have I ever taken a physics class. I am doing a study on the effects of noise pollution on wildlife. Thanks!

Answer 1

after some algebra, your formula can be rewritten as:

d1/d2 = e^((spl2 - spl1)/20)

or maybe more usefully:

d1 = d2*e^((spl2 - spl1)/20)

Now you have it. I hope that helped.

By the way, I'm assuming you meant "natural log" when you wrote log. If you really meant log (base 10) then you'd have:

d1 = d2*10^((spl2 - spl1)/20)

Answer 2

For SPL in db, the log is base ten.