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why does the presence of a CATV cable connected to a different input on the receiver cause a hum when a different input is hooked to the PC sound card, and (b) continues to do so even when the PC is turned off, but plugged in?
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Let me ask you a question: What is an antenna?
Answer: A long piece of metal strung through the air in the hopes of picking up electro-magnetic signals.
What is a CATV coax?
Answer: A long piece of metal cable strung through the air in parallel with 60 hz power wires.
While it does not intend to be an antenna - CATV coax strung between houses acts like an antenna and picks up 60 hz humm. This is ignored by the CATV equipment, but it contaminates your electronics with a signal in the audio range.
Does that help explain things?