The traditional method of removing broken taps in a toolroom is to turn a rod
from soft material such as aluminium to core size of tap , make a little well of
plasticene around tap position , fill it with coarse grinding paste then set up the rod
in a drilling machine and use it and the grinding paste to grind through the tap .
Works in minutes if you do it right and and hole is usually undamaged .
Spark erosion is the cleanest and fastest method by far but the equipment is
not readily available even in industry .
On the ultrasound question I have heard of this but what actually happens is
a combination of two things – the tap gets heated and if carbon steel it may be
enough to soften the metal and the multiple impacts would tend to loosen the tap in the hole . This is one of those many quirky things read about once somewhere and then quickly forgotten because its useless in practice .