You can also test shear forces on the bar, a test you can perform easily at the bank itself (or any of the other material forces tests really). Those do usually require a bit of machinery.
Lastly, you can measure electric resistance. A gold bar will have a different resistance than a tungsten bar, especially if you compare a frequency sweep AC resistance vs DC resistance (if there is a difference, which should be about 20nOhm/m vs 50nOhm/m for Gold/Tungsten, you know the material has a core that is different from the outside).
Electric current mostly travels on the surface of a material. Gold-plated tungsten might not have sufficiently different resistance from pure gold, if the plating is thick enough.
The higher the frequency the less you penetrate the material (self-induction in the material forces the electrons outwards).
This enables you to effectively do a sweep of material composition by increasing frequency and measuring the resistance. In theory you could even tell if the core was not conductive at all (due to the resistance not changing despite lower frequency).
So even if the plating was thick, you would be able to tell because the resistance curve begins to change at lower frequencies due to Tungsten having a higher resistance.
If your device is really accurate you could even measure the rough area of the core since skin effect is proportional to the square of the resistivity.
Considering how expensive gold is per ounce, it's not like any of us will be buying it by the bar.
Executive Order 6102.
If you're in a country where you can't trust the government, you lost. The government can take away your gold, your government can take away your bitcoins.
If "the government has become the enemy" is a problem, then you've got bigger problems at hand.
Actually, it's not. It's nearly impossible to non-destructively distinguish gold from tungsten wrapped in gold.