Loud low sounds can travel very far, especially at night when it’s quiet. I can hear freight trains at night that are over 5 miles away. It wouldn’t surprise me if the beam engine was louder than a freight train, and that nights were even quieter in the early 20th century. Hundreds of miles is a bit much though.
Train at 5 miles is nothing. Can confirm.
There are confounding factors of course, like direction and what's in between. E.g. do you sleep in a room that's on the opposite side of the house with windows closed and good insulation/windows? You'll probably be totally fine.
Do you sleep in a room that's towards the source and with the window open? Oh you will very very much hear that train, especially if the wind is coming from that direction.
Sleeping outside? Oh you will very much hear that train!
The engine would have been significantly less noisy than a diesel locomotive. It's almost eerie how quiet they can be, given how big they are.
The pump it drove could have been loud, though.
If the train is moving at the right speed the carriages will hit any bump in the track at a frequency that resonates.
You get the same effect over a smaller area with vibratory compactors used in construction. Get the frequency just right and the whole neighborhood can feel it.
I too can hear distant trains at night, especially if it is a still, clear night creating a low-level inversion to channel the sound.
There are several places in Britain (and elsewhere, I imagine) where beam engines have been preserved and are periodically run using live steam. the engines themselves are quiet by modern standards, though I believe the machinery they drove often produced a racket.
I can hear the start-up of 777 engines at the airport, every night at approx. the same time. The airport is 12 km from my apartment and there's a hill in between. But my bedroom is facing the airport side and the wind mostly comes from that direction. It's crazy.