# How does air pressure affect the ability to create a frequency and which frequency is least attenuated

From $$I=ξ^2ω^2cρ$$ where ξ is the particle displacement, ω the frequency, c the speed of sound and ρ the density of the medium (1, 2), I understand that for the same frequency and amplitude the sound intensity increases with the pressure/density of the air. Would getting that same frequency and amplitude require more energy, more effort (moving denser air), or because the intensity is greater since the air pressure is greater would that mean you can use less effort to create the same level of sound (or would they cancel out--more effort to make a sound because the air is denser but less effort because intensity increases with pressure)?

Also, attenuation. I found a chart showing attenuation related to humidity for 1 atmosphere which indicates that as humidity rises, the absorption coefficient rises, but it is for 20 degrees C--I need to figure out for different temperatures at a chosen pressure and humidity what would be the absorption coefficient.

Trying to figure out how far, realistically, two people on the surface of a planet with fairly Earth-like air (breathable, i.e.) could communicate in an atmosphere of 2.5 bars with high average humidity over a range of temperatures. (High daytime temps, low nighttime temps, the range of which I have not worked out yet as I need to work out how much heat such an atmosphere would hold during the day and how quickly it would radiate it out to space on a cloudless night but that's a problem for another day.)

Finally, probably the composition of the air may make some difference, changes in percentages of Oxygen, Nitrogen, and Carbon Dioxide, but I am willing to not consider those at this time--a breathable atmosphere similar to Earth's is sufficient.

• Maybe you should add some more information in your question. For example, where did you find this formula, for which cases is valid, and what each letter denotes. To my knowledge, the intensity is not given by the same formula for all cases in acoustics. For example a cylindrical source "sees" different impedance than a spherical one. Commented Oct 3, 2021 at 9:41
• Good point. Added where I got the information. I am considering the case of being on a planetary surface, so a spherical source is probably more relevant for one person on the planetary surface speaking to another (assuming breathable air, just denser). Commented Oct 3, 2021 at 10:22