I can't recall seeing any reference to this in any of the Star Trek series, but it seems inconceivable that the air pressure on board the Enterprise would always be the same as where the crew was transporting to or from.
Because this transition is effectively even faster than that of a landing airplane, their ears must pop every time, right?
Although it's totally hand-waved in the show and films as being one of the things that the transporter just does (along with removing momentum) this issue has been addressed in at least one of the TNG novels.
In Indistinguishable from Magic, Captain Geordi LaForge is trialing a new faster transporter system. Apparently one of its key failings is that it works too quickly to allow the normal process of air pressure equalisation:
Captain’s Log, Stardate 60214.1. Since Tyler Hunt’s memorial service and the completion of the Challenger’s repairs, we have been on an extended detachment to test a new transporter upgrade that’s intended to provide near-instantaneous transport. No visible materialization phase, just pop, and you’re there. I’m sorry that that doesn’t really sound technical enough, but it’s the most accurate description of that I’ve heard so far. The ideal is that the full dematerialization and dematerialization phases should, together, take no more point zero two of a second. So far, the technology works, but the pressure differential caused by so quick a departure or arrival has — according to the results from testing with human-analog test objects — burst eardrums and caused other pressure-related problems. As a result, the program has gone back to the drawing board at the Daystrom Institute, and Challenger, I hope, will be free to resume a duty that, I don’t mind admitting, I find more appealing.
If the pressure in the transporter room is the same as the pressure where you're beaming to your ears would not pop. I've never seen or heard of anything that states that in a Federation Transporter room the pressure is equalized to the destination. However keep in mind that your ears would pop once the pressure in the transporter room was changed, and whoever is running the transporters at the time would have ear popping pretty regularly each time a transport started, he/she walked out of the room, etc. So they'd pop before being transported.
If it's not pressurized in the transporter room it would be virtually impossible to pressurize the destination location. Are you going to pressurize an entire planet or large enough area that the person wouldn't be affected? The transporter isn't going to displace that much space and it would immediately shift back to the original pressure even if the transporter were capable of such a feat.
The third possibility is the transporter does something to you internally to adjust your ear drums, eustation tubes, etc. That would seem not possible, but transporters don't really make sense anyway, at least in the Star Trek universe, remember it's Science FICTION.
The answer above with the passage about Geordi needs further explanation as to the context. I'm assuming what Geordi is saying is that as a person goes through transport the environmental pressure around them slowly changes so it won't be an abrupt change. The transporter converts matter to energy (pattern+energy stream whatever that means) and then back to matter. I'm not sure exactly how atmospheric pressure would play into that or be converted into energy. Pressure is not a thing you can transport, it's a condition based on certain scientific principles. Either way, the change would be the same for the person whether it takes .02 seconds or 2 seconds. Your body doesn't adjust any different to those small time increments.
I took college level physics, chemistry, organic chemistry, physics, botany, and electronics. I took those classes at a top 20 university at the time, albeit it was a long time ago. So I'm not going to put citations for what are essentially scientific facts.
Hope I didn't confuse things more. :)
It's one of those little details that you aren't supposed to pay any attention to.
The air pressure in the transporter room set is always the same as the air pressure in the planetary-surface set, so the problem never came up in a way that required explanation on screen.
