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The idea behind something appearing is more visual in nature; it comes into sight.
What would I say if something "appeared audibly"? The sound of the oncoming car appeared to my ears!
Synonyms for appear all seem to stick to visual, material, or abstract concepts; nothing for auditory elements stand out.
Stick with simplicity. I propose go.(Oxford, sense 4.2)
Make a sound of a specified kind:
the engine went bang
The elevator went ping and the doors opened.
It was dark. I couldn't see anything. Suddenly, I heard a gun go bang.
Speaking of guns, go off is related:
(Of a gun, bomb, or similar device) explode or fire:
(Of an alarm) begin to sound.
And then, I heard an alarm go off in the distance.
In case you're not still convinced, watch this.
Assuming you're asking for the sound equivalent of:
A light appeared in the forest
to become manifest : become known
Along with "arise" or "emerge," you could use "ring out."
"Pistol shots ring out in the barroom night."
Or, along with those, and if you aren't talking about a sound, you could use sound as a verb. Like this:
"The trumpets sounded from the other side of the room."
But maybe don't say: "The sound sounded from the other side of the room." Unless you're after that.
A word that's sometimes used is arise. As in the line from A Visit From Saint Nicholas:
When out on the lawn there arose such a clatter,
I sprang from my bed to see what was the matter.
Emanated
You can have "a person appeared from behind the wall" as well as "a sound emanated from behind the wall".
Along with "emerge", you could use "arise"
a : to begin to occur or to exist : to come into being or to attention
Emerged is taking over in usage, though, vs. arose, when paired with "sound"
You might try looking up the comparison for your specific example.
To clarify the difference between verbs that reference the production or perception of a sound or image:
Like appear (and emerge), arise references the perception of its subject (to come in sight, to come into attention, to become known).
Appear, 1 a : to be or come in sight
when the sun appears on the horizon
Compare to the verb sound, which references the moment of sound production
transitive verb 1 a : to cause to sound
sound a trumpet
intransitive verb 1 a: to make a sound
"Appear means to come into visual consciousness"
and
Hear means to "perceive with the ear the sound made by (someone or something)."
"Behind her she could hear men's voices"
verb: hear; 3rd person present: hears; past tense: heard; past participle: heard; gerund or present participle: hearing
When used as a verb sound can mean (ODO):
Emit or cause to emit sound
[no object]: a loud buzzer sounded
[with object]: she sounded the horn
Similarly to the way to appear is used for visible objects, e.g.
A magnificent sight appeared in front of their eyes
there are examples of usage for to sound
This chiming... Which I've had sounding in my ears for ten years
from: Strindberg and the Five Senses by Hans-Goran Ekman
or
Another and other hoofs than Puck's sounded in my ears close ... and crushed against mo-a sharp pain smote through my chest—a roar sounded in my ears- horses seemed to be about and around me on every side, and it was all darkness.
from: London Society, Volume 8; Volume 10 James Hogg, Florence Marryat
(emphasis mine)
Per the OED, Fade-in is:
...the gradual... increase in the brightness or definition of a picture or the loudness of a sound.
A more poetic, if not literal, word would be Coalesce:
To bring together, merge; to combine (parts or elements) to form one whole.
Though it does not use the word Coalesce, I always think of Salieri's quote from Amadeus, which I think captures the spirit of it:
On the page it looked nothing. The beginning simple, almost comic. Just a pulse, bassoons and basset horns, like a rusty squeezebox. Then suddenly; high above it, an oboe, a single note, hanging there unwavering, till a clarinet took over and sweetened it into a phrase of such delight!
"The sound became audible." Other ways it could be phrased are: "I began to hear the sound of ...", "I became aware of the sound of ...", "The sound of ... slowly entered my awareness." or possibly "The silence was broken by the sound of ..."
"A faint noise which quickly evolved into the thrumming of an engine."
"I could hear the faint noise of a car coming in the distance."
"A faint noise which quickly turned into the distant sound of a car coming down the road."
Resound -
re·sound
rəˈzound/Submit
verb
1.
(of a sound, voice, etc.) fill a place with sound; be loud enough to echo.
"another scream resounded through the school"
synonyms: echo, re-echo, reverberate, ring out, boom, thunder, rumble
"the explosion resounded around the silent street"
Alternatively a source independent descriptor for something to appear, emerge, or develop could be the word arrive which could apply to sound.
Depending on what you're after, then crescendo might be what you want.
From https://en.wiktionary.org/wiki/crescendo:
Verb. To increase in intensity, to reach or head for a crescendo.
An example from http://www.dictionary.com/browse/crescendo:
Then his ears caught a crescendo of the whispering that he had heard before.
The Whispering Spheres, Russell Robert Winterbotham
