What are the characteristics of a voice that make it different from other voice, in terms of properties of the sound wave ?
The direct answer is very generic:
- Frequency: Changes in wave frequency relate to pitch/intonation
- Amplitude: Changes in wave amplitude relate to stress and pronunciation
But that is pretty much the answer to every other "What are the characteristics of X that make it different from other X'es, in terms of properties of the sound wave?"
The more interesting aspects are the harmonies and resonances, or formants. The formants are formed by chamber and tube resonances, which is what makes us able to distinguish the different vowels. But the formant "weight" or tendency of a voice is also what makes it very characteristic (and the main difference between male and female, along with pitch) (source).
Check out this interactive formant/vowel app
In terms of wave properties formants describe how multiple frequences relate and work together.
The thing that makes one voice sound different from another is the same thing that makes a trumpet sound different from a tuba: the different size and shape of the instrument. That produces a dramatically different sound wave. You’ll get a different frequency spectrum from each voice. Imagine a trumpet, a slightly bigger trumpet, a slightly longer trumpet, and so on for 7 billion more trumpets until you get to a tuba. Every one of them will make the spectrum on an EQ light up slightly differently.