It should be straightforward to make an acoustic time of flight go/no go meter you could place on a gold bar. Piezo excitation transducer/fixed distance/piezo receiver/process signal propagation velocity -> light up red or green light.
According to those numbers for a ~10cm bar you'd need ~1 microsecond resolution, or more depending on your tolerance of the tungsten mixture (for 1% tungsten-platinum alloy substitution you'll need ~10ns resolution).
I'm not sure this is easy to achieve! A best case commercial speaker/microphone will have a ~100khz bandwidth, which gives ~10 microsecond resolution. If you're aiming for high accuracy you also need to account for thermal variations in speed of sound, which would require a some precise thermometers.
I suppose don't use a speaker/microphone then. Use a laser reflected at an angle off the bar to an optical transducer and strike the bar. Watch for the initial strike and the reflection. The time domain is nothing for a dedicated CPU such as the 64MHz one I use in my projects. If the only issue is sensing the phenomenon, I'm sure something could be devised.
What, run up and down the street naked, yelling Eureka?
Actually, I'm agreed that you could measure the density, but somebody could fiddle with the density too by adding just a touch of this or that to bring everything up to the right weight.
Random sample. I'm not familiar with gold bars, but I imagine that there are procedures for this (like rectifying at a new weight or recasting the sampled bars). A few milligrams of gold shouldn't be a big deal unless we're dealing with gold fever.
If you're willing to melt them down though, you probably don't have to deal with mass spec as some property will have to give (melting point, density, etc).
You can't determine if the gold bar is salted by only measuring its density. It's pretty easy to create a mix of gold, tungsten and osmium to have the exact same density as pure gold.
If I was a bank dealing with standardized gold bars, I'd make a machine that validates a bar at the push of a button. Surely they have that, given that a single 40 Oz bar is worth $800,000.
I wonder if the acoustical properties of a fake bar would be easy to distinguish from solid gold.