When you and someone else keep waving back and forth, that's a Wave Ping-Pong. Each back-and-forth is a rally.
Only your first wave to a new person counts towards your daily waves.
Waving back in a rally doesn't use up a wave.
You can wave again as soon as they wave back. Otherwise, you can wave at the same person once every 24 hours.
If you both wave, a chat opens too, so you can say more than hello.