While I cannot put a label on it right now (but surely it has a name, read about it somewhere), it is some kind of paradox that sufficiently advanced civilizations will broadcast themselves openly and detectably only for a very very tiny fraction of time (tens of years are nothing on intergalactic, interstellar or even planetary scale).

We quickly learned that blasting long-wave analog voice signals to the skies and expecting the reflection behind the horizon is pretty inefficient and moved to shorter, shorter and shorter waves. Not only you don't need to blast local radio stations in local language to the other side of the planet, having hundreds of computer wireless networks in one apartment building means that it actually shouldn't broadcast more than a few walls away in order for multiple networks to coexist even with time-division multiplexes and collision avoidance magic.

So, in about a hundred years, we discovered RF, we then started by blasting long-wave radio stations using ionosphere as a mirror, gradually moved to more and more local frequency bands, we then launched satellites to wirelessly ping across the ocean, only to hide the signals back under the sea and ground using fiber optics for practical reasons (bandwidth, latency), we went from analog to digital and we started encrypting just about everything. In the end, we will produce mostly random noise with ultrashort reach.

Next step - we will enclose Sol with Dyson sphere and disappear completely :)