It used to be a loose core in the flyback transformer that generated the high voltage for the cathode ray tube. All the children in the house would hear it, but the older adults often couldn’t. I wasn’t aware that satellite television sets still needed them. 😀
Though flyback transformers aren’t needed in modern TVs, something very like them is very common! Almost all modern power-supplies are switch-mode.
Rather than have a heavy iron-cored transformer at 50Hz, the mains is rectified and used to power an oscillator running at about 100kHz. A transformer running at that frequency is tiny, and doesn’t need an iron-core. Switch-mode supplies save power. An idling 50Hz transformer wastes about 10% of it’s rating, whereas the electronic version wastes less than 1%, your mileage may vary!
Nothing is perfect. The transformer in a switch-mode PSU can vibrate audibly if it or the windings come loose, and the oscillator might drop temporarily into the wrong mode, making it whistle. The box and circuit board have resonances that the transformer might reinforce. Turning the power off and on disturbs the resonance, and the whistle stops.
Maybe!
Dave