How would the law determine acceptable noise levels of neighbors?

Seems like anytime someone has a loud neighbor the police always want the two parties to settle it between themselves and the “how loud is too loud” question is a massive gray area.
If two parties were at complete odds with one another how would a court decide what is an acceptble noise level?
Say you like to sit in your backyard after work, have a drink and read the paper.
Your neighbor is 50 feet away likes to do the same thing but has a radio and likes to play techno music every day. It’s not blasting but you can’t escape not hearing it.
How about if a neighbor has a stereo in their garage they like to play that has low bass? With your windows and doors closed and TV on low you can still hear the low thump-thump of his stereo. Once again if you step outside the music isn’t blasting but it definately is audible.
What’s the line in the sand or rule of thumb for noise tolerance in a suburban setting?

The law is different for each community (city, county and state).

When I used to manage a historical property rented out for weddings, our rule of thumb was that 65 dB at the edge of the property was too loud and we’d go shush the partiers or their DJ. However, the formal law was really vague. We were technically zoned commercial but with residential neighbors. Essentially, the law said that anything that bothered the neighbors after dark was against the law (no matter how quiet), and anything we did during the daytime was legal (no matter how loud).

I think the general concensus is that if you got a call from the neighbor, it’s loud enough to be worth a warning, and if you have multiple calls, it’s loud enough to be worth a citation. If you disagree with the citation, you have the ability to explain your case to a judge who may overturn the citation.

I highly doubt cops carry any instruments to measure sound levels precisely, and I highly doubt the law states the sound level precisely. Sometimes things are just a judgement call.

The problem with noise between neighbors is it’s subjective. Assessment of noise depends on who is producing it. It is easy to feel indignant when you are asked to turn down your ‘noisy’ radio - but complain bitterly about your neighbor when the same volume drifts across the fence into your property. And yet you will hardly notice a jet airliner, three or four times louder, as it passes over your head. And this gets to the heart of the problem. It is not noise which is bothering you - it is a perceived invasion of your privacy. The closer we live to one another, the more territorial we become and the quicker we are to take offence. Having lived in the UK in small ‘terraced’ houses, I have personal experience of how quickly one can feel ‘murderous’ toward your neighbor on the other side of a paper-thin party wall.

So what is the answer? Apart from a civil request to your neighbor - and a self-admission that nothing short of switching his music off will truly satisfy you - there is not a lot to be done. Going to the Courts is unlikely to produce anything constructive.

Mark Twain “A dog is that which is recognized as a dog by other dogs.”

Noise violations are whatever is recognized as a noise violation by people who decide what noise violations are. if it’s not obvious, then obviously the police would rather not be in the middle.

Not sure what rememdies are generally available.

Many communities have standards written into the statutes that noise may not be more than x decibels at y feet. Rules of thumb are trumped by the law.