I presume, from the size of the car park and the huge circle of snow-covered seats, that Old Faithful draws as many visitors today as ever, but the day we were there was bitterly cold and the snow was so thick that most of the roads in Yellowstone National Park were closed. Only the road to the Norris Basin and that down to Old Faithful were being kept open by constant ploughing.
There is a sign in the Visitor Centre telling you when the next eruption is due, which for us was just 23 minutes away. We brushed the snow off one of the seats, buttoned up our coats, and waited.
The eruption was three minutes early, an aberration for which we didn't complain. The thin tendril of steam gradually grew thicker and higher and then, suddenly, steam and boiling water erupted out of the vent and the cloud of steam soared high into the sky.
As far as the sight was concerned, it was pretty much as we had expected. What we hadn't expected was the near total silence! We thought an erupting geyser, especially one as large as Old Faithful, would go off with a sound like the Flying Scotsman letting off steam, but all we got was a gentle "whoosh"ing rather like an electric kettle on its last legs.
So no, there's nothing wrong with the sound in the video: what we heard is what you get.