I did a sound degradation experiment in which I played model sounds from a speaker and the re-recorded at 4 distances (1, 35, 60 and 100m). I would like to estimate the distance in which sound intensity will go below background noise somehow extrapolating SPL. I have measures of signal-to-noise ratio and SPL for each sound at each distance. I have tried models using a single SPL value/distance but the result changes a lot depending on which distance is being used. So I am looking for a way to take into account all distances.
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asked Oct 4, 2023 at 16:24
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plot the SPL as function of log10(distance) and extrapolate linealy to the background SPL.
explanation: pressure decreases with 1/distance^2. a log-log plot will then generate a linear relation. SPL is already logarithmic, so you only need to use log10(distance). In absence of absorption and other effects (wind in air, reflections) the slope the function will be -2. Any small deviation may be due to absorption, larger deviations are most likely due to reflections.
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$\begingroup$ Yes, this is a good solution, but I would advise caution regarding the measurements made at 1 m distance. These recordings are likely to be in the near field for the low-mid frequency portion of the spectrum (for various definitions of low-mid depending on whether you'r measuring in water or air). Near field is sometimes defined as the region where inverse square-law is not appropriate. If I recall correctly the rule-of-thumb is that near-field is anything closer than 4 wavelengths, though I've also recall others saying 6 or 7 wavelengths. $\endgroup$– Brian Miller ♦Commented Oct 5, 2023 at 2:01