This^^^ is the best answer so far.
There is no finite distance, too many other factors have an affect on how sound travels.
Of course, but that doesn't mean there can't be reasonable assessments. I am currently thinking I'll focus on 1/4 mile from my house. As I said we are close to a hospital with sirens, heavy traffic both on the freeway and a major 4-lane street most of the day. We have a flat landscape but lots of shady and sound-absorbing trees.
I would ask why do you want a cockbird?
How important is it to you vs. ticking off your neighbors?
I want a rooster a) because I'd like to free range my hens more and want the protection for them, b) because it's a more natural and complete part of the chicken experience and c) because they're beautiful.
Ticking off my neighbors -- or, more correctly, NOT ticking off my neighbors -- is
very important to me. For that reason I would give communicating with them in advance my best shot. That doesn't mean that I have any illusion that I can please everyone but if my closest neighbors feel strongly I'd give that
serious consideration. But ultimately I will make a choice I can live with.
For many years our immediate next door neighbor had a horse on a 1/2 acre lot. Since we are live-and-let-live people, we sucked it up and dealt with the odor that sometimes made enjoying an outside meal challenging. That doesn't mean I believe everyone is as tolerant as I am but it
does mean that I believe in the relaxed character of my neighborhood and people's ability to cope.
Hard to poll folks, they might say it's fine then call the cops when it disturbs them.
Trying to silence, or quiet down, a crower is pretty much futile and can be cruel to the crower.
If they don't take the opportunity to reply or to be up front about their objections then it would more or less fall to them to suck it up, no? If they called the police to object I'm sure they'd hear what I'd tell them which is that we are zoned for a rooster and would be within the same category as someone who has a dog who barks or a motorcycle or any other nuisance.
OTOH, if it becomes a bigger issue over time, there is a feed store that will take roosters.
I have no intention of using a device to inhibit crowing.