In the second formula above, the value of “10 Log (Q/4πr2) + 0.2” can be represented by “C”. It then becomes Lp = Lw + C or Lw = Lp – C. Substituting into the first formula, W = 10-12 x 10(Lp – C)/10.
When there are two noise sources, e.g. machine (m) noise and background (b) noise, the value of C depends on the surrounding condition of each noise source and its location from the measuring point. For background noise, it is of a multi-source nature and difficult to identify the source surrounding condition and location. We may take it as originating from the same location as the machine noise so that the values of “C” are the same for both sources.
Referring to the scalar nature of sound power and the machine/background noises mentioned in the preceding paragraph, the combined sound power Wr arising from the two noise sources is simply the sum of their respective sound power Wm and Wb, i.e. Wr = Wm + Wb.
With the combined and background sound pressure levels in hand upon taking the necessary measurements, we can start off to find out the machine sound pressure level through manipulation of the above-mentioned formulae. We have: