I have a Sony sports radio, and I thought the earphones were bad because I
always had to jiggle the cord near where it plugged in I replaced the
headphones, but I have the same problem with the new pair, although it is
not quite as bad as the old pair.

So, I am guessing that the jack receptacle itself is loose, not the wire.

Is there a way to fix this? Can I wrap alum. foil around the male end? Or
tape? I know it is an inexpensive radio, but if there is a simple way to
fix it, I'd love to forego the expense of a new one.

Thanks.