Not so, unfortunately. Atomic weight is not the same as density. Atomic weight is the weight of one mole , or 6.02 x 10**23 atoms, of a substance. Atomic weight says nothing about the volume occupied by one mole of a substance so you can't just weigh two bars of equal size and expect a 5% difference in weight if one is gold and the other tungsten.
Yes, indeed. Thanks.
Au = 19320 kg/M*3
W = 19600 kg/M*3
Since W is more dense, this whole thing gets tough.
Go for the ultrasound solution.