Try coiling up part of a mike cable into an orderly solenoid coil, NOT
scramble wound. You can put it on a pop bottle or other pipe form for a
test. If that works, you can measure and compute what inductance it was
and replicate it with a ferrite core, passing the mike cable thru and
around that for fewer turns.
If you want to get deep into the radio, see if there are ferrite beads
on the mike connector wiring, and if not, add that. Beads web sites
usually have application notes on how much equivalent inductance you get
per bead and you can put multiple beads if there is room. Insulate the
beads from contact with chassis or other conductors.
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