People on Reddit are corroborating Hackett’s account, and others sub-tweeting him lament the strange noises as well.
As of now, though, the actual reason for the hissing noise is unknown, and speculation is running wild on the web. Many people, such as Ars Technica’s Stephen Anthony, are chalking the noise up to coil whine -- which occurs when electrical components create an audible sound after over processing. To be fair, it’s the same noise that any desktop computer or laptop makes, although hearing the noise from a smartphone is weird. Some message boards are swarming with complaints of "freaky noise."
As Anthony indicates, the issue could also stem from radio frequency interference with the phone’s audio system -- which has undergone an extreme makeover since the headphone jack was removed. The Verge notes that the noise might stem from the phone’s A10 processor, which is bigger and more powerful than ever before.
The larger takeaway from this is that there’s really nothing to be that concerned about. If the noise is bothersome, you can follow Hackett’s example and replace your iPhone via AppleCare. Many in the tech blogosphere are fearing a “Hiss-Gate” controversy, as the floodgates open with hyperbolic complaints about the new iPhone. But don't count on it -- after all, the phone still brand new.