Why do I have 120v coming out of a 240v cable
simulate this circuit &ndash; Schematic created using CircuitLab

I strongly suspect you have an amplifier with an input transformer with taps for both 240V and 120V, as in the diagram.  That way, it can be configured in the factory for either 240V or 120V use, without having to re-design anything - just swap a wire from one terminal to another.

If that's the case, then you're seeing the primary of the transformer act as an auto-transformer.  If you put 240V into the 240V tap, then you'll get 120V out of the 120V tap.