I don't usually have this kind of problem, but I'm writing about a space shuttle reentry, and I'm not sure how to properly explain this. Just as the little four-person shuttle hits the atmosphere and begins to get all fiery and shaky, the pilot starts to play 'Magic Carpet Ride' by Steppenwolf over the speaker system. But I can't say the title of the song, and even if I did, some readers might not get it. How could I describe the mood of that song accurately inside the cabin without going over the top?
I would think that the crew must do a lot of check lists and such, so they cant get up and dance. Why not just say whoever played the song, then quote a line or so in italics. I actually don't think there needs to be any reaction. If someone changes stations in a car, what sort of reaction would you have? Do the same thing.
David Webber did something like this in his second Honor Harrington book. Everyone on the ship was busy trying to repair severe battle damage, knowing that within hours they would all be dead if the enemy came at them one last time. So the Captain put on some symphonic music on the non-priority channels for the crew to listen to. Webber, kept this part short only two or three paragraphs, mentioning how the music reminded various characters of their home planet, with its harsh melodies followed by tranquil parts. It also said how some of the crew looked up startled upon hearing the music and then went straight back to work. I wish I could remember more about it, but it's been a few years.
You could always have something take place in the cabin that reminds one of the crew members of that particular song, then have that crew member start singing or humming it, which in turn sets the mood for the rest of the crew.
You can show it by the reactions of the crew, and describe the music with description like a pulse-pounding rock classic. That way, without even naming the song, you've established the mood arising from it.