I'm glad I'm not the only one! I got my new iPhone 7 Plus in Black (at&t) this morning. I noticed it when I was testing out the new speakers. I put my ear up to the top speaker while the sound was at the lowest setting and it seemed like there was static coming from the speaker. But after playing around with it a little more, it's definitely not from the speaker. Like mentioned, I hear it the loudest when I put my ear up to the top-right of the back of the phone (the side opposite the cameras. The noise is there regardless of charging or not charging and regardless of phone being locked or unlocked. The noise gets louder (or the frequency changes?) and fluctuates depending on what you're doing but it's always there. It was also there when I tested my phone call, but the noise was reduced and not too noticeable. Placing phone in Airplane mode reduces the noise quite a bit it is still there. The noise seems more prominent when doing something processor-intensive or data-intensive.
Everything else about the phone works perfectly. I have been using it all day and it has behaved. Very fast, very responsive, fast LTE and Wi-Fi downloads. There are no other defects as far as I can tell. You can't hear the noise unless you put your ear close enough to the phone, but it's just really strange. It was hard enough to get a black 7 Plus on launch day, and now to try and get a replacement that might do the same thing? I don't know if it's worth it. I wonder if it could possibly be something funky with the modem firmware or something else that could be corrected via a software update?
I know that obviously a phone should not be emitting strange noise from internal parts, but I don't want to exchange it if a lot of these phones are doing the same thing. Obviously I'm not the only one, and there's probably even more who don't even realize it since you have to listen closely. I guess I'll wait a few days and see if more come out stating they're having the same issue. Maybe Apple will address it if it's widespread enough.