# Sound Folks: A Basic Error in Your Calcs? **URL:** \ **Category:** Factual Questions\ **Created:** [November 9, 2008, 12:25pm UTC](https://boards.straightdope.com/t/sound-folks-a-basic-error-in-your-calcs/471895 "2008-11-09T12:25:53Z")\ **Posts on this page:** 9\ **Page:** 1
**Author:** ![Jinx](https://avatars.discourse-cdn.com/v4/letter/j/c6cbf5/32.png) [@Jinx](https://boards.straightdope.com/u/Jinx)\ **Post date:** [November 9, 2008, 12:25pm UTC](https://boards.straightdope.com/t/sound-folks-a-basic-error-in-your-calcs/471895/1 "2008-11-09T12:25:53Z")
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. - Jinx ---
**Author:** ![ZenBeam](https://avatars.discourse-cdn.com/v4/letter/z/3ab097/32.png) [@ZenBeam](https://boards.straightdope.com/u/ZenBeam)\ **Post date:** [November 9, 2008, 12:45pm UTC](https://boards.straightdope.com/t/sound-folks-a-basic-error-in-your-calcs/471895/2 "2008-11-09T12:45:46Z")
> [@Jinx](#): > > a) dB-PWL = 10 log (watts /watts ref); using watts = 1W and watts ref = 10e-12. Is that really 10E-12, or is it 1.0E-12? ---
**Author:** ![Jinx](https://avatars.discourse-cdn.com/v4/letter/j/c6cbf5/32.png) [@Jinx](https://boards.straightdope.com/u/Jinx)\ **Post date:** [November 9, 2008, 12:46pm UTC](https://boards.straightdope.com/t/sound-folks-a-basic-error-in-your-calcs/471895/3 "2008-11-09T12:46:25Z")
FYI: My Ref is “Sound System Engineering” by Don and Carolyn Davis, 1st edition, 12th printing, 1986, p.40. The publisher is Howard W. Sams Co (a division of Macmillion) of Indianapolis. 1st edition printed © 1975. ---
**Author:** ![Jinx](https://avatars.discourse-cdn.com/v4/letter/j/c6cbf5/32.png) [@Jinx](https://boards.straightdope.com/u/Jinx)\ **Post date:** [November 9, 2008, 12:51pm UTC](https://boards.straightdope.com/t/sound-folks-a-basic-error-in-your-calcs/471895/4 "2008-11-09T12:51:12Z")
> [@ZenBeam](#): > > Is that really 10E-12, or is it 1.0E-12? While I see this makes all the difference, my reference and others ALL state it this way as 10e-12. ---
**Author:** ![Jinx](https://avatars.discourse-cdn.com/v4/letter/j/c6cbf5/32.png) [@Jinx](https://boards.straightdope.com/u/Jinx)\ **Post date:** [November 9, 2008, 1:08pm UTC](https://boards.straightdope.com/t/sound-folks-a-basic-error-in-your-calcs/471895/5 "2008-11-09T13:08:08Z")
Zen, you’re correct…I think I was mis-entering 10^-12 as 10e-12 into my spreadsheet…when it should really have been entered as 1e-12. ---
**Author:** ![firstname](https://avatars.discourse-cdn.com/v4/letter/f/7ab992/32.png) [@firstname](https://boards.straightdope.com/u/firstname)\ **Post date:** [November 9, 2008, 1:26pm UTC](https://boards.straightdope.com/t/sound-folks-a-basic-error-in-your-calcs/471895/6 "2008-11-09T13:26:38Z")
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. Maybe this is a newer version than you have, [Sound System Engineering - Don Davis, Carolyn Davis - Google Books](http://books.google.com/books?id=9mAUp5IC5AMC&pg=PA43&lpg=PA43&dq=db+pwl++%2B120+db&source=web&ots=vycHse3Wb2&sig=ronyYmeQ_MwUsYwn5gzzfL0RCn8&hl=en&sa=X&oi=book_result&resnum=2&ct=result#PPA47,M1) There is clearly an error somewhere. ---
**Author:** ![Jinx](https://avatars.discourse-cdn.com/v4/letter/j/c6cbf5/32.png) [@Jinx](https://boards.straightdope.com/u/Jinx)\ **Post date:** [November 9, 2008, 2:55pm UTC](https://boards.straightdope.com/t/sound-folks-a-basic-error-in-your-calcs/471895/7 "2008-11-09T14:55:31Z")
> [@firstname](#): > > 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. > > Maybe this is a newer version than you have, [Sound System Engineering - Don Davis, Carolyn Davis - Google Books](http://books.google.com/books?id=9mAUp5IC5AMC&pg=PA43&lpg=PA43&dq=db+pwl++%2B120+db&source=web&ots=vycHse3Wb2&sig=ronyYmeQ_MwUsYwn5gzzfL0RCn8&hl=en&sa=X&oi=book_result&resnum=2&ct=result#PPA47,M1) > > There is clearly an error somewhere. 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 ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [November 9, 2008, 6:44pm UTC](https://boards.straightdope.com/t/sound-folks-a-basic-error-in-your-calcs/471895/8 "2008-11-09T18:44:42Z")
> [@](#): > > This is an old mental block for me that 10^-12 = 1 x 10^-12 = 1e-12 \<\> 10e-12. 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. ---
**Author:** ![Jinx](https://avatars.discourse-cdn.com/v4/letter/j/c6cbf5/32.png) [@Jinx](https://boards.straightdope.com/u/Jinx)\ **Post date:** [November 10, 2008, 1:18am UTC](https://boards.straightdope.com/t/sound-folks-a-basic-error-in-your-calcs/471895/9 "2008-11-10T01:18:34Z")
> [@Chronos](#): > > 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.