I wanted to bury my approach deeper in the thread rather than offer it first because I wanted to encourage people to offer their elegant solutions.
1.) I consider thunder damage to be more concussive vibration than sound, but they're still quite audible. When I describe thunder damage, it comes with more of a focus on the vibrations and bursting energy first, and the audible impact second.
2.) I used the 2d8 (average 9) of Thunderwave audible at 300 feet and 1d6 (average 3.5) of Thunderclap audible at 100 feet as benchmarks. Yes, that assumes low level casting. I added a third point of reference - 0 damage at 0 feet, then used the quadratic equation and rounded things off. The equation I received was
thunder damage can be heard at distance in feet, in 'normal' conditions, equal to (damage squared) plus 25 times the damage. This gets us pretty close to 3.5 damage Thunderclaps being heard at 100 feet, and 9 damage Thunderwaves being heard at 300 feet. Using this formula, 50 thunder damage can be heard at 3750 feet.
3.) I overwrite this formula where another distance is specified (Thunderwave is always 300 feet, even when upcast) or where the text description calls for it (some spells make it clear they're loud). This is a judgment call.
4.) I generally figure it out based upon average damage rather than looking it up for every damage roll. However, if there is a really unusual damage roll and the sound could change the situation, I look it up. This has only taken place a handful of times in the last 2 years that I have been using this technique.
5.) Then I apply my judgment as to how muted (or amplified) the situation is based upon the conditions. For me, normal conditions are outside in a moderately filled setting such as a forest or a city with little sound pollution. The more noise pollution is present, or if there is dampening due to surfaces, I'll treat it as if the damage were less (resulting in a smaller area) - usually either half the damage or a quarter the damage.
With this applied: A Sapphire Dragon's breath can be heard in the wild from a bit over a half mile. A Steel Predator's roar can be heard from a quarter mile away. A sorcerer that swaps thunder damage for fire damage in a Meteor Swarm makes something that can be heard from a mile and a quarter away. A Booming Blade going off at low levels is ~ 125 feet, but might be as high as ~750 feet at higher level.
And for me, in this respect, a lightning bolt that is soundless would be very weird. Or a fireball that creates no light (although I agree what it will not illuminate a distant wall, it should be visible from far away).
For me this is less of an issue as I do not picture a lightning bolt as thunder and lightning, but instead as the arc flash, like in a mad scientist laboratory. I describe them with
zot and
zap - not
boom. However, I get why others see it the other way.