@thor I'd be willing to bet its the powersource. Your speakers are likely using a switching power supply running at 4 khz.. the reason is a few 1) thats typical for guitar amps 2) the harmonics are typical of a square wave, which means your seeing RFI from a PWM like in a switching power supply.
So my top guess right now with like 80% certainty is that it is the power supply to the amp (if its a wall wart its that, if its a straight plug its internal).