Spike:
Wow lots of comments. I too would like to comment as well. By definition, for Sound Pressure Levels, SPL=20log(p/pref) Re 2x10-5 N/m^2. This definition can be stated another way, SPL=10log(p/pref)^2. If we remember that for this last definition, the squared pressure ratio is based on "power-related" quantities (that is, p^2), this confusion can be avoided.
By way of a simple EXAMPLE_1:
Consider the effect of adding another machine in an area where other equipment is operating. Assume that the ambient sound level due to the other equipment is Lp1=90dB and the level from the machine to be added is LP2=88dB. Estimate the combine level.
SOLUTION:
Lp=10log(p/pref)^2 -or- (p/pref)^2 = antilog(Lp/10)
Thus,
(p1/pref)^2 = antilog(90/10) = 10^(90/10) = 10 x 10^8
(p2/pref)^2 = antilog(88/10) = 10^(88/10) = 6.31 x 10^8
(ptotal/pref)^2 = (p1/pref)^2 + (p2/pref)^2
(ptotal/pref)^2 = 10 x 10^8 + 6.31 x 10^8
Lptotal = 10log(16.31 x 10^8) = 92.12 dB
The same principle applies, when attempting overall sound pressure levels from 1/3-octave bands.
Lptotal = 10log(p1^2 + p2^2 + . . . + pn^2 / pref^2)
Lptotal = 10log(10^(p1/10) + 10^(p2/10)+ . . . 10^(pn/10))
Check your calculations! Record the individual SPL 1/3-octave band levels of some known source. Then, hand calculate the overall SPL. Check the overall value as recorded by the analyzer - hopefully success!
Regarding random vibration, this is somewhat more difficult, however, similar logarithmic equations exist.
EXAMPLE_2.
If you know that your overall PSD level of a profile is say 3.315gRMS. What would be the overall PSD level of say a profile that is +3dB?
Recall,
Level = 20log(PSDnew/PSDref)
PSDnew = PSDref x antilog (Level/20)
PSDnew = PSDref x 10^(Level/20)
Thus,
PSDnew = = 3.315 x 10^(+3/20) = 4.683gRMS
I hope this helps.
Thanks,
Kaiserman