In the documentary, they explained that T.rex was more closely related to birds and crocodilians, who don't roar like T.rex has often been depicted doing (ex. Jurassic Park). Crocodilians, in particular, make low frequency sounds, and T.rex's ears were designed to pick up those sounds. Therefore, it would have had a low frequency-type roar. T.rex has been depicted as roaring like a mammal, but T.rex would have sounded like a bird or crocodilian, mainly a crocodilian. The researchers in the documentary gave the T.rex a modified Chinese Alligator vocal, and it resulted in sounding like a demon out of hell... or the Jaws theme song. Imagine that? If Spielberg took his Jaws theme and give it to the T.rex in the Jurassic Park movies, then he would have given the T.rex an accurate roar!
In my opinion, I think T.rex would have sounded like an American Alligator, since both of them lived in North America. However, it would have been an even deeper version of the American Alligator's vocals. Maybe it would have been a combination of an alligator's and another bird's vocals (a bird that makes low frequency calls), but I think T.rex's roar would have definitely sounded like a deep Alligator growl.
Update (2/27/20): I think I've found a bird that T.rex might've sounded like: A cassowary. These birds have surprisingly deep vocals. Therefore, I think T.rex might've sounded like a mix between an alligator and a cassowary.
Alligator Vocals 1:
Links:
The Real T-Rex with Chris Packham (at 33:30-39:20):
https://www.dailymotion.com/video/x6d590l
Alligator Vocals:
Video 1:
https://www.youtube.com/watch?v=bXTlmnjGx0Y&t=48s
Video 2:
https://www.youtube.com/watch?v=H2l0Flg5WFc&t=122s
Cassowary Vocals:
https://www.youtube.com/watch?v=4dcQO6Zb8Eg
Phil Center (2009) ("Abstract," and "The big picture," p. 7):
https://www.tandfonline.com/doi/full/10.1080/08912960903033327