What is the relationship between the reach of a RF signal and its frequency?
What I mean is: If power is kept constant, should I use high or low frequency waves to get a better reach? Why?
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In free space, it doesn't matter. The power per incident area of a propagating wave is inversely proportional to the square of the distance from the transmitter. This is true regardless of frequency.
Certain frequencies are reflected, refracted, absorbed, and scattered differently by different materials. There is no single monotonic relationship until you get to really high energies, like gamma rays and beyond. At these really high energies (high frequencies), the waves basically just blast thru any material in their way, with higher energies passing thru material with less attenutation. Up to below Xray frequencies, there is no single answer, and it depends on the material between the transmitter and receiver.
Diffraction effects can make low fequencies (long wavelengths) appear to bend around objects, but this actually occurs at all wavelengths. The "near" layer where diffraction effects occur scales with wavelength, so it appears to us at a fixed human scale that long wavelengths go "around" objects where short wavelengths don't, but that is due to our perception scale. On the scale of the earth, commercial AM radio frequencies around 1 MHz are low enough to diffract around the curvature of the earth to some extent making over the horizon AM reception possible. Commercial FM radio, being 100x shorter wavelength, exhibits this effect much less for the same size earth, so FM radio appears to us to be mostly occluded by the horizon.
You are looking at a quite deep topic called radio wave propagation.
From what I understand, low frequencies can follow the curvature of the earth (ground wave) and can get around obstacles more easily due to their larger wavelength. Higher frequencies are often restricted to line-of-sight propagation.
"Free-space propagation of a waveform between antennas is completely independent of frequency"
However, apart from the above mentioned effect of low-frequencies following the curvature of the earth, another common reason why lower frequency signals get better communication distances is that their quarter-wave (or other type) antennas are physically larger, giving a larger "effective area" in the antenna equations, and better coupling between transmitter and receiver.
Besides from what has been said by the others (in free space frequency doesn't matter, if there is not free space absorbtion, refraction, diffraction, scattering etc. has to be considered and those dependend very much on frequency and the matter inbetween) it will also be important how easy it is the construct effective antennas for the frequency you use. You need to get the power somehow into the space and out of it.
E.g. if you want to use a rather low frequency in order to penetrate into matter (e.g. below earth or sea level) but it is very difficult to build antennas for such low frequencies (several km wavelength).
Thank you for your interest in this question.
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