Jeff Liebermann wrote:

40KHz thru 285Khz? Great idea. Just one minor problem. A 1/4 wave
antenna at about 100Khz frequency is 750 meters long. That's going to
be a rather large antenna for literally dragging behind you.

Well, your math is correct. However, the so-called "atomic" wrist
watches receive their time signal from WWVB which transmits at 60kHz.

How do they get that 1250 meter long antenna ( 1/4 wave at 60 kHz)
inside that itty bitty wrist watch case? ;-)