Gold is soft, so you can probably push a needle inside to check for a tungsten core (most common way to fake gold bars)

Not as fancy as X-ray techniques, but much cheaper and readily available

Maybe you can analyse the propagation of mechanical waves within, not sure (so a pure gold bar will 'sound' differently when struck with a soft mallet)

Yes, X-ray fluorescence. Modern handheld devices are fast, accurate, and relatively inexpensive, see my other post.

Might be worth noting that the things denser than gold are probably all going to be more expensive as well, so there isn't really any way to hollow out your gold and fill it with weights to correct the density. Even DU falls short of being dense enough todo that.

Tungsten has a density extremely similar to that of gold (19.25 g/cm³ for tungsten, 19.30 g/cm³ for gold), and is substantially less expensive. And tungsten counterfeiting does happen: http://www.zerohedge.com/news/tungsten-filled-10-oz-gold-bar...

Detectable if you measure density carefully enough (though do people? I don't know). If you did that with plutonium instead (way more expensive than gold obviously, so it would be a silly thing to do) then you could get it as close as you wanted.

As an interesting sidebar, there's a series of photos of some of the scientists on Tinian posing with a small box containing the core of the Fat Man bomb - a 3.5" diameter sphere of Plutonium that was apparently worth at the time the equivalent of about $5 billion dollars.

http://nuclearsecrecy.com/blog/2011/11/25/friday-image-posin...

It's certainly detectable with precise instruments, but it's not practical to test each and every bit of gold one acquires so thoroughly. Hence the opportunity for counterfeit gold that passes casual inspection and weighs about the right amount.

And DU would be ...?

EDIT: I think you meant Tungsten, also known as Wolfram (symbol W): http://en.wikipedia.org/wiki/Tungsten

Gold: 19.30 g/cm3 (http://en.wikipedia.org/wiki/Gold)

Wolfram: 19.25 g/cm3 (http://en.wikipedia.org/wiki/Tungsten)

EDIT2 (I can not reply to your reply): So you meant Depleted Uranium (http://en.wikipedia.org/wiki/Depleted_uranium)

Depleted Uranium: 19.1 g/cm3

So Wolfram is a better substitute for Gold, in terms of density. I do not know about prices or other physical properties.

Pretty sure they meant Depleted Uranium by DU. http://en.wikipedia.org/wiki/Depleted_uranium

Has a lower density than Tungsten, though so would make a poor counterfeiting material in both cost and physical properties.

Sorry yes, depleted uranium. Tugnsten also comes close, but not close enough to get it perfect. If you can accurately measure density you could still detect that.

The question I suppose is does anybody measure density carefully enough to detect tungsten, and if not, should they be?

Yeah that's already happening. Look up gold plated tungsten.