Thanks for the tip. I hooked up my VCR to my TV. I don't know where to plug in the cord for the picture, but I do have a red/white hook-up, so I was able to hear the sound from the VHS tape.
There is **no** high pitch noise when I play the VHS on my TV. I have a Bose sound system from years ago that's still in great shape; I put my ear right against the speaker and the sound comes through fine. That means it's... Roxio? My Mac?
Another note that might be important: If I have Roxio open on my Mac and pause the VHS, I can still hear the high pitch noise. This is probably the easiest way for me to hear the noise because it doesn't compete with the tape's audio. While the VHS is paused, if I unplug the red/white cords from the Roxio USB device, the ringing remains. But if I leave the red/white plugged in and unplug the S-Video cable from the Roxio USB device, the ringing stops and (obviously) the paused screen goes blank.