Rock Gnomes possess the capability to produce small devices such as the "Clockwork Toy", "Fire Starter" and "Music Box". The book specifically states that they produce sound. My expectation on how I would personally use this is as a distraction. So from how far away are these devices Audible?
There are no rules governing sound and audibility.
And at first I thought this would be a simple "rulings, not rules" matter in 5e. "C'mon, have you ever heard a music box?" I thought. "Just figure it out in ten seconds with your GM and move on." But...
There are a lot of things that depend on sound/audibility. Enough that maybe there should be rules on it.*
As a brief survey, we've got many Bardic class features, many charms/enchantments, turning undead/faithless, Battle Master maneuvers, Blindsense, the Inspiring Leader feat, and the "Unseen Attackers and Targets" section of combat... and dozens of spells!
Turning to the DMG, "Noticing other Creatures" (p.243) would be a nice place to find a bit of suggested rules--but it's silent. It does tell us that "if neither side is being stealthy, creatures automatically notice each other once they are within sight or hearing range of each other." And that's it. Never a discussion about what a reasonable hearing range might be.
So it's worth developing a decent system. I'll leave that to you and your GM, but here are the relevant touchstones I see:
- 30': many effects key off of a creature/target being able to hear you and being within 30'. The strong implication is that "normal" noises can be heard at 30'.
- 30', 60', 120': sentient items may possess sight and hearing, and their hearing may extend to 30', 60', or 120' (DMG p.214). Thus these are not unreasonable ranges, though they are magically-created ranges and need not be taken for gospel.
- 300': The various Thunder-based spells (and Knock, but excepting Thunderclap (100')) specify that their unusually-loud effects are audible out to 300'. This, then, presents a range at which it'd be unreasonable for "normal" noises to be audible.
* @KorvinStarmast rightly points out that my suggestion that one should develop a more-systematic approach to sound and hearing goes against the explicit 5e design philosophy of trying to simplify, staying away from excessive simulationism. My suggestion that one might codify this is based upon the surprise I felt when I discovered just how important sound is, just how many mechanics do key off of it. You, of course, should play your game. And enjoy!
RAW have no explicit sound and audibility rules
The rules1 are silent on any mechanical detail regarding "how far away the two Gnome items can be heard." That means that it is up to the DM to rule on, which is a common 5e D&D approach: rulings over rules.
Music Box. When opened, this music box plays a single song at a moderate volume. The box stops playing when it reaches the song’s end or when it is closed.
For the Music Box, "moderate volume" is as descriptive as it needs to be for the game. The "noises as appropriate to the creature it represents" is likewise left for the DM to assess the detail. (Appropriate would include the point that for a dog it barks, for a cat it purrs, etc).
From a simulationist perspective, this makes a lot of sense. Hearing is an interaction between the source and the receiver modified by the environment, unlike a spell effect that has a range from the source (caster). The range at which you can hear something is a combination of
How sensitive your hearing is
How loud the thing is (dB / sound pressure level)
How much background noise there is in the area.
Your ability to concentrate on listening.
Consider the phrase "it was so quiet I could hear a pin drop."
Most of the above considerations are folded into passive and / or active Perception check.
Some Creatures Hear better than Others
On the "how sensitive your hearing is" test, some creatures have much better hearing than others. The attributes "Keen Hearing" and "Keen Senses" give a mechanical bonus (Advantage on Perception checks involving hearing) for those monsters with that attribute. Other attributes, such as Tremorsense or Blindsense, are not cited as having a direct impact on a die roll for a perception check, but the DM could certainly rule that they help the roll.
Example: Dire Wolf
Keen Hearing and Smell. The wolf has advantage on Wisdom (Perception) checks that rely on hearing or smell.1
Keen Senses. The pseudodragon has advantage on Wisdom (Perception) checks that rely on sight, hearing, or smell.
You would expect that a Dire Wolf or a Pseudodragon would hear the gnome's music box at a greater range than a human, thanks to the attribute of Keen Hearing or Keen Sense.
You'd also expect an elf PC to hear it from further away. It is interesting to note that "Keen Senses" in the case of the elf offers Proficiency in the perception skill, not advantage on the rolls.
If you intend to use the toy or music box in game as a distraction, it might be best to do two things:
- Discuss this with your DM ahead of time. What you don't want to do is try to surprise the DM with it and possibly get into a rules-and-their-effects argument that disrupts the flow of play.
- While playing, make sure you ask the DM about the background/setting to get an idea of how much or how little background noise is present in the situation where you try to use the toy in a tactical manner.
Tremorsense and Blindsight considerations
Tremorsense. A monster with tremorsense can detect and pinpoint the origin of vibrations within a specific radius, provided that the monster and the source of the vibrations are in contact with the same ground or substance.
A DM might rule that Tremorsense aids in detection range for simple hearing, depending upon the situation.
For a 14th level Rogue (PC) Blindsense might provide an advantage or bonus to hearing, or not, per a DM's ruling. The class ability seems to fold in a lot of sensory inputs, but it does cite hearing as a criterion.
... if you are able to hear, you are aware of the location of any hidden or invisible creature within 10 feet of you.
1 Rules referenced are SRD. Page 6, rock gnome items; page 366 Dire Wolf Keen Hearing; page 343 Pseudodragon Keen Senses; page 260 Tremorsense ; page 40 Blindsense; page 4 Elf Keen Senses
There is some guidance on the DM's screen
If you assumed the sound level was "normal", the audible distance would be about 70' on average, "quiet" about half that, 35' and "very loud" about 350'.
These line up pretty well with @nitsua60's proposed system.