Interesting question from a customer.
They were post weighting Z-weighted octave data to get A-weighted octave data and then summing.
They were seeing a noticeable difference between the directly measured A-weighting value, LAeq, and the value they got from summing the octave data
Applying A-, C- or Z-weighting to 1/3- or 1/1-octave band data and then summing to get an overall value assumes that the data is “pink” within each band.
How close to “pink” the noise is a decision for the noise consultant. Sound like traffic noise is generally flat but noise from wind turbines or jet aircraft have significant tonal components.
The issue with post-weighting is it applies the A-weighting of the center frequency of the 1/3- or 1/1-octave band. The A-weighting curve has a steep slope at frequencies below 1k Hz. For example, the 500 Hz 1/1-octave band (355-710 Hz band-pass) has an A-weighting of -3.2 dB at it 500 Hz center frequency, relative to Z- or C-weighting, but is -4.8 dB at 400 Hz and only -1.9 at 630 Hz. Attached is a table showing A-weighting values at 1/3-octave frequencies.
If noise is not “pink” across the 500 Hz band, applying the A-weighting correction value at 500 Hz will give either a too high or too low value.
Post-weighting 1/1-octave has a wider band-pass so is more problematic than post-weighting 1/3-octave data.
Note: this is not a significant issue when simply summing 1/1- or 1/3-octave data and comparing to an overall value without post weighting. Just be careful to sum across the same frequency range for the 1/1- or 1/3-octave data as the pass-band for the overall.