Why did my car make a noise at a particular RPM?

Problem was fixed under warranty, so this is not an advice thread. I’m just curious. At 2000 RPM, a noise would come from the back of my car, kind of a high pitched whirring. It was diagnosed as stemming from loose exhaust covers (or something or other like that–I left the invoice at my office so I can’t say exactly what it said). So something back there was loose, and under the right circumstances was producing a noise. That’s clear enough. But why would it produce the noise just when I was at the 2000 RPM mark?

It had nothing to do with speed or rate of acceleration. It was specifically correlated to RPMs.

It’s resonance. The frequency of the sound waves in the exhaust depend on engine RPM - the faster the engine spins, the higher the pitch. The loose exhaust covers had a resonant frequency that was close to the pitch of the exhaust at 2000 RPM.

Sometime set a bowl of water on your console and then slowly raise the rpm level and watch the pattern in the water. You can often see the pattern develop rough areas at different rpms.