High frequency For example, I try to chase wild animals by creating a high sound pressure level with a frequency of 17 kHz or higher, but I can't calculate the initial sound pressure. One thing is because it seems that the attenuation of sound pressure level in the air varies according to the frequency, so it is not possible to do a sufficient calculation with just the inverse square law of sound. If you want to guarantee 140dB with a frequency of 17kHz or higher at a distance of 500m, I would appreciate it if you could tell me the formula how to calculate the initial sound pressure.
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2$\begingroup$ Hello Midas, did you do any research prior to posting your question? If yes, let us know what you currently have, and why it is not sufficient for your needs. Because a very quick google search gives me this page en.wikipedia.org/wiki/Stokes%27s_law_of_sound_attenuation which seems to answer all the points in your question. Also, stack exchange provides a list of questions related to yours where it seems that you would definitely find an answer to your question as written. $\endgroup$– Barbaud JulienCommented Jan 24, 2022 at 5:58
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1$\begingroup$ See for example this question which clarifies that Stoke's law and the inverse square law describe two different effects (dissipation in a medium vs. spreading of the energy) and should be taken as complementary to each other, although for propagation in air you can pretty much neglect dissipation and rely only on the inverse square law. $\endgroup$– Barbaud JulienCommented Jan 24, 2022 at 6:03
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Just to quickly answer your question... No, it doesn't.
Inverse square law just like Barbaud Julien state in their comment, inverse square law has to do with the spread of energy in space. At least in linear acoustics, the law is frequency independent. As long as the point source model is an adequate approximation for the real source it should provide good results.
What you seem to be talking about is the total sound pressure level at a specific distance from source. In this case there's two different "things" you have to take into account. One is energy spread (the simplest case being inverse square law of course) and the other is energy dissipation (attenuation in practice). It is easy to calculate the inverse square law up to a distance adequately close to the source (the law has a singularity at the position of the source). From there you would have to resort to the calculation of some sort of near-field calculation, most probably involving the energy/power of the source.
Next, you should also include attenuation in your model. You could either resort to some mathematical models (which, to my knowledge, can be quite complex since they deal with molecular relaxation states) or use some values from plots and tables. Since you are interested in a single frequency, I would suggest you use some tabular values, at least at a first stage. If this is deemed inadequate, then you could move on to a more precise and complex mathematical model.
More information about sound attenuation in air can be found in this Physics SE post, this webpage (an online Mathematica notebook solution is also provided for convenience) and references therein which are this paper and ANSI S1.25:1995. You may also find this calculator to be useful.
