Tao of D&D's talks about Hearing Checks.
GURPS B358 has a similar table but only in ranges. Decibel reference would be useful.
Since the Average person should be able to hear this in the distance given, the Basic Task Difficulty Modifier would be +4 (routine or mundane). In D20 this would be a DC5. when circumstances have more Stress and Distractions then you can have TDM +0 or worse and for D20 about DC10 or worse.
False SensationsNote that in the real world we have false sensations of sounds, especially when we are expecting it. The cool thing about this is that you can make failed rolls, quirks or disads, play in the way of false sensations.
in Fast Twitch Games and in Combat Simulations like Airsoft, we have a Ton of Sensation Noise and False Sensations. When I first began I was struggling to filter these out, and we learned a lot from our Captain and in about 7 years of playing.
There is this thing called Pareidolia and the Cognitive "hacks" our brain has to increase our response time by gaming the statistics its a foe before confirmation results in friendly fire. I've had about 4 friendly fire incidents where I accidentally took out an ally in 7 years of airsoft and a innumerable number where I was lucky not to hit them.
Friendly Fire and Decision Making is well discussed in The Art of Critical Decision making by Micheal Roberto in chapter 20 Practical Drift.
In the Game
What does False Sensations mean? It means the GM can F*ck you up.
Seriously the GM can pull out sensations from inside his @$$ and play it on a character with disads and a circumstance that would fit well. Verification of information is a SKILL, which can be summed up by GURPS observation skill or a Multi-Sensory Skill like perception in some games.
Getting back to the Game Applications of False Sensations - PCs will needs skills to verify and Noise is part of the game. This incentives a well rounded character or Old School Player Skill Virtues.
I don't know where "ROLE-players" stand in Problem Solving exercises, because I get the impression such Versmilitude gets in the way. I on the other hand, I believe Information asymmetry adds to the believability and realism of a Story, because life is without enough certainties and too many doubts. Making bad decisions that hurt yourself, loved ones, your team, and your career, because of many distracting and noisy factors is just Simulative Decision making that pushes us to think of better strategies or try out other strategies.
Its nice to Know that because of the growing number of people playing RPGs thanks to Roll20 I may find other like minds who will help me and each other grow and learn better problem solving through the games.