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Modeling the effect of atmospheric attenuation on a propagation outdoor noise

Noise due to explosions can be represented by a Gaussian pulse containing all frequencies. The low frequencies tend to be attenuated significantly less than higher frequencies and can therefore travel over large distances measured in kilometers. To understand the effect of the frequency-dependent attenuation of the outdoor noise on the shape and amplitude of the propagated pulse, we assume three models of frequency dependence of the atmospheric attenuation (frequency-independent, proportional to absolute value of the frequency, and proportional to the square of frequency). In each case, we compute the effect of the attenuation on the Green's function, the propagation over a hard flat surface, both in the frequency and in the time domain. We also show that for practical frequencies and distances and in a uniform atmosphere, the method for calculation of the absorption of sound, is best approximated by an attenuation model that is proportional to frequency squared. In all cases, the impact on the shape of the pulse is characterized but is found in general to be minimal. Curiously, the constant attenuation case is the most effective, while an attenuation coefficient that is proportional to the squared frequency is the least effective because this latter case favors high frequencies and ignores the low frequencies, which are the more important frequencies for long-distance atmospheric propagation.