I've been trying to DIY a home audio setup. We have a pair of speakers in the ceiling of an upper floor (previously installed), and a new TV on the same floor. We wanted the sound of the TV to come out of the speakers.
The speakers are connected to an amp in the basement, and there are existing CAT5 cables running behind the new TV down to the basement. Rewiring is challenging, so we took advantage of the existing setup and got a cheap pair of audio-to-CAT5 baluns (https://www.amazon.ca/LINESO-3-5mm-Stereo-White-Extender/dp/B01HHO8382), hooked one side to the TV (3.5mm jack) and the other side to the amp in the basement. The TV sends audio to the audio-out port, through the balun, through the CAT5 cable, back through another balun, to the amp, which amplifies the sound and sends it to the speakers.
Now, for the fun part: when the TV is on, everything works great. But, if the TV is turned off and the amp is set to a loud enough volume, there's an audible mains hum (~60Hz) over the speakers. My best guess is that the CAT5 cables are picking up small currents from the mains over their length (not surprising as they run through multiple floors). When the TV is on, the TV's line out presumably sinks these stray currents (if not playing anything) or otherwise produces enough current to drown out the induced currents. When the TV is off, it disconnects its audio output; the amp's 47kΩ input is high enough and has high enough sensitivity to amplify the induced currents into a buzzing noise.
What can I do to reduce or eliminate the unwanted sound, ideally with a passive solution? I have thought about adding a resistor somewhere but I am not sure whether it would be in parallel or in series with the connection, nor what value it should have.