A bullet traveling at 3000 feet/second doesn't "zing". What you hear is more like a crackling or ripping sound, as the bullet breaks the sound barrier.
And, by the time you heard it, it would already be past you or in you.
I can tell you've never been shot at, or not very much. Many calibers can sound ZING when they go by, others CRACK, and so on. A big factor is how far they've traveled before they get to where you're at. I speak from experience. Handguns, Rifles, and yes, even shotguns. Some are scarier than others.