To be clear, I am arguing radio waves, electromagnetic radiation, not sound waves. I am stating that electromagnetic radiation travels until it is either scattered or absorbed. Therefore, if a radio wave travels through space without being absorbed or scattered, it will travel indefinitely.
Your naked eye contention is just false. Stand in a desert, a flat desert, and look to the horizon. The naked eye only sees the reflected light that has not been obstructed, and therefore, usually can only see about 2 to 20 miles out. That, however, does not mean the light information has deteriorated in the distance to be unrecognizable, that just means the reflected light has been obstructed, scattered or absorbed.
An unobstructed radio wave, will travel indefinitely in space.
Just curious. If what you are saying is true, and supported by the scientific community, why are cosmologists hopeful on the idea that if there is intelligent life out there, they hope the life will pick up our signals and be able to interpret our message and send something back? Based on what you are saying, all scientists who think this are wrong. And I find that hard to believe.