It does appear to be a transmitter rather than receiver,but not for direct radiation,as there is no aerial to be seen.The connections to power on the pcb conform with your suggestion of some sort of modulation of the power line Guy?
The hole in the case is to gain access to an adjustment preset,as though perhaps some "tweaking" needed doing sometimes.
Usually,with anything like this,there would be all sorts of notifications on the case to say that the device conforms with certain regulations pertaining to connection to mains.That there are none means it's a home build,praps from a magazine article?
Was your Father a techie?
The matching 'speaker is lost presumeably?
Nick