The Pingcoin app performs a sound-based test. It records and analyzes the frequency content of the sound produced by your coin and compares it with what it knows about the authentic coin you're testing it against. The frequency content of a coin's sound is dictated by two properties: (1) the coin's geometry (i.e. thickness, diameter and relief) and (2) the coin's material properties (i.e. density, elasticity, compressibility and homogeneity).
If either the geometry or the material properties are off, the verdict will be inconclusive. If the test returns with a positive verdict, then that means both the geometry and the material properties fall within a range that is to be expected for authentic coins of the variant you're testing.
Although almost all counterfeits will diverge from the allowed geometry or material properties, there are certain non-authentic coins that could still pass the test. There are two main categories of non-authentic coins that could still pass the test.
The first is unofficially minted coins with correct diameter and material properties. If a coin has the correct diameter and thickness and is also minted from the same material (e.g. gold or silver) with the correct composition, then its frequencies will be indistinguishable from an authentic coin. Historically, when the premium on certain gold coins rose, it became profitable for counterfeiter to mint their own gold and silver coins. Instead of making money by replacing the gold and silver content, they minted coins with the officially designated amounts of gold and silver, but passed them off at a premium, pretending they were official coins.
The second type of coin that might pass the test are what we call collision verdicts. One of the limitations of the ping test is that the frequency content of a coin's sound isn't like a fingerprint, but more like a musical pitch. Put differently, a coin's sound profile isn't unique, some overlap between coins of different geometries and material classes does occur. This intuition for this is that you can have a bronze flute and a wooden flute that produce the same pitch. For this to happen they need to have wildly different geometries, but it is possible. What isn't possible, is a wooden and a bronze flute with the same geometry, to produce the same pitch. The same is true for coins. You can have two coins of different material and different geometry that produce the same pitch. What cannot occur is two coins with the same geometry, but with different material properties, producing the same pitch.