I don't know exactly who came up with the 5kHz frequency for gold. Possibly Bill Morgan (BMI detectors). To my knowledge, it is not the result of any calculations, nor does it relate in any way to the NMR frequency.
Most likely, it was derived through experimental methods using known samples, and finding frequencies where dowsing rods reacted the strongest. Such experiments, where good scientific methods such as randomized blind testing are NOT used, produce results that are entirely subjective, and will vary wildly person-to-person. I have no doubt that whoever came up with 5kHz, would fail miserably to confirm that frequency in a randomized blind test.
Also, of the MFDs I've looked at, I've yet to see one that actually uses 5kHz for gold. Even stranger, I've yet to find any two models that use the same frequency for gold. Even models from the same manufacturer -- 3 from Dell and 2 from Vector Trek -- are different. And some of Dell's have a knob that vary the frequency all over the place. It's truly as if the frequency makes no difference whatsoever... and it doesn't. It's all just a big hoax.
- Carl