There are two formulas to yield dB-PWL, but results differ by 10 dB-PWL. Yet, my reference from noted authorities, Don and Caolyn Davis, says the formulas are the same. Maybe someone has a clue what’s up? Here are my findings:
a) dB-PWL = 10 log (watts /watts ref); using watts = 1W and watts ref = 10e-12.
This yields 110 dB-PWL.
b) dB-PWL = 10 log (watts) +120 db; using watts = 1W
This yields 120 dB-PWL.
I find formula (a) = formula (b) - 10 dB! What’s up? Is the author in error?
FYI: More references quote formula (a). It is well accepted while I’ve never seen formula (b) cited anywhere else.
Any information or suggestions the SD can provide may help me piece things together would be great.
A googlebook of your textbook shows it as 10^-12, and has it yielding 120 db,(which as you state is 110db) (page 43) but it also shows on page 47 an “old” standard reference of 10^-13 (Which gives 120 when calculated) and a “new” standard reference of 10^-12.
No, no…I have to admit the error is mine. This is an old mental block for me that 10^-12 = 1 x 10^-12 = 1e-12 <> 10e-12. As for the old standard, that is true BUT the 10^-12 was then re-defined as the standard since it relates to 120dB. I don’t have my book in front of me now, but IIRC, the newer standard of 10^-12 best related the scale to the human ear’s range of hearing. - Jinx
If I had a dollar for every time I saw a student make that mistake… Well, I don’t know how much it’d come to, but I’d make more than all the other TAs.
It’s the way it was taught to me (ages ago) that “e” simply means exponent that creates the confusion. If “e” meant exponent, then 1e2 = 1^2, but it does not. Hence, the confusion.