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If the ringtone is inherently funny, then Embarrassing Ringtone.
If the drowning out is meant to be the funny part, probably Sound-Effect Bleep (although this is normally used to cover up swearing, Shrek the Third used it to cover up Fiona trying to tell Shrek that Fiona is pregnant).
I mean, I feel like Interrupting Phone might be a trope in and of itself regardless of how funny it is; the phone interrupting the song of Don't Hug Me I'm Scared 5, for example. It jars people out of the action and can be funny or dramatic.
Currently Working On: Incorruptible Pure Pureness
Kinda Busy Here but it doesn't cover the drowning out crucial information aspect.
Edited by eroock
Hmm, Kinda Busy Here covers a lot of it, but would it cover examples of peoples phones interrupting things in classrooms, theaters, and other less actiony scenes?
"It's just a show; I should really just relax"
"No Talking or Phones" Warning sometimes features examples of what you're looking for as reasons for turning off your phones, but it's not exactly about what you're looking for.
If not for this anchor I'd be dancing between the stars. At least I can try to write better vampire stories than Twilight.
A gag where someone's cell phone keeps interrupting things by going off at inappropriate or important moments, often drowning out crucial information.