What is the reason that high frequency radio wave experience more attenuation compare to low frequency radio wave? Is high frequency experiences attenuation at high distance or at low distance?
Actually it depends on which frequencies and the propagation environment.
As Digiproc says correctly at higher freqs the atmosphere absorbs more. This is mainly true above 18 GHz, and as you go up it a absorbs a lot more. There are absorption windows (i.e., less absorption) in a band somewhere in the 30 to 40 GHz region and then up at about 94.
Below 18 GHz down to about 10 GHz it goes down (less absorption), and from there down to KHz it basically is transparent (some absoprtion still). If you go low enough to the HF band you get ionospheric reflection and absorption. You can get most of that in a couple graphs in books.
Dependong on your application other things are more important. For instance, for terrestrial ground to ground propagation the scattering, reflection, diffraction and absorption of vegetation and man made object is more determinative. Lower frequencies get absorbed less, and diffract more so go around objects. From 2-4 GHz there some of that, but then worse up to 10 GHz. So, for so called non-line of sight propagation lower frequencies, even below 2 (HZ and down to and in,coding VHF are better. In wireless comms the preferred frequencies are around 700 MHz because they penetrate buildings more. Yes, at lower frequencies you have more multipath degradation (multipath interference) but you can process a lot of that out with some freq and code diversity, and MIMO.
But if you want GHz bandwidths you have to go higher. So it all depends on what you want.
If empty space they all go like $1/r^2$. At lower freqs you do need bigger antennas, if you want the same beam size. if omni unless you go to HF and below its no big deal. At real high freqs, above 100-1000 GHz you are now in the THz band, and the device physics/engineering is non-trivial. Even above 100 GHz it's not trivial.
There is no attenuation in free space, no matter what the frequency. Other mediums (like the atmosphere) have their unique attenuation spectra. For radio frequencies, there is more attenuation through the atmosphere for higher frequencies because they are better absorbed by the moisture in the air.