Separating A Noise Source
from the Background Noise

By TK NG

        When measuring the noise levels at different octave bands of an operating machine such as air-cooled chiller on site, what you can get are the combined sound pressure levels of the machine and the surrounding background.  To allow analysis of the characteristics of the machine noise for devising noise mitigation measures, the background noise must be discounted.  So, the background noise octave band pressure levels have also to be measured upon switching off the machine.

        Separating the background noise from a machine noise is by no means simple arithmetic, but you would agree it is not that complicated once you have reviewed the relationship between the different parameters associated with a particular noise.  What can be measured directly is the sound pressure level, but it is the sound power (acoustic energy) that allows us to add or deduct directly.  We must therefore resort to the formulae defining the relationship between sound power and sound pressure levels for analysis.

        Let us look at the formulae for sound power level and its relationship with sound pressure level:

        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:

        If the measured Lpr and Lpb are 75dB and 70dB respectively, the Lpm is 73.35dB as calculated from the above formula.  For Lpr = 65dB and Lpb = 60dB, Lpm is 63.35dB.  Also, for Lpr = 85dB and Lpb = 80dB, Lpm is 83.35dB.  Looking at the patterns exhibited in these figures, you may wonder if there is a simple algorithm that can save you the trouble of having to go through the logarithmic calculation in the process.

        The good news is that there is a simple set of rules as shown in the table below for determining, to a reasonable degree of accuracy, the combined sound pressure level of two noise sources.  You can test its validity using the re-arranged formula Lpr = 10 log (10Lpm/10 + 10Lpb/10).

        The above does not apply to certain circumstances, e.g. when two noise sources are in-phase, the resulting sound pressure level may increase substantially.  Conversely, if they are out-of-phase, they may cancel each other completely.

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