Cum tibia in atrio sonare incipit, infans ridet.

No. This cum is a conjunction, not the preposition meaning with.

Here it means when and introduces a time clause:

• Cum tibia in atrio sonare incipit = When the flute begins to sound in the atrium

Latin cum can have several meanings depending on how it is used:

• cum + ablative = with
• cum introducing a clause = often when, sometimes since or although

In this sentence, it is clearly the conjunction when.

Because incipit often takes a complementary infinitive in Latin.

So:

• incipit = begins
• sonare = to sound

Together:

• sonare incipit = begins to sound

This is very similar to English begins to sound.
Latin often uses verbs like incipio (begin), possum (be able), debeo (ought), and volo (want) with an infinitive.

If Latin used sonat instead, that would give a different structure and meaning.

Because tibia is the subject of incipit.

In other words, it is the thing that begins to sound.

• tibia = nominative singular
• it is a first-declension noun

So the clause works like this:

• tibia ... incipit = the flute begins ...

A learner should also know that tibia can mean:

• flute / pipe
• or shin-bone

Here the context clearly shows the musical meaning.

Because in takes the ablative when it means in/on a place where something already is.

So:

• in atrio = in the atrium

This is a standard Latin distinction:

• in + ablative = location, in / on
• in + accusative = motion toward, into / onto

Compare:

• in atrio = in the atrium
• in atrium = into the atrium

Here there is no movement into the space; the sound begins there, so the ablative is used.

The sentence has two parts:

Subordinate time clause:

• Cum tibia in atrio sonare incipit
• When the flute begins to sound in the atrium

Main clause:

• infans ridet
• the baby laughs / smiles

The cum clause gives the time or circumstance for the action in the main clause.

Because this is a straightforward temporal use of cum meaning when.

The verb is:

• incipit — present indicative

In basic Latin, cum with the indicative often gives a simple factual time relationship:

• when X happens, Y happens

By contrast, cum with the subjunctive is often used in more literary or nuanced clauses, especially ones that are:

• circumstantial
• causal
• concessive

So here the indicative is the natural choice for a simple statement of time.

Because Latin word order is much more flexible than English word order.

English depends heavily on word order to show meaning. Latin depends much more on:

• case endings
• verb endings
• context

So Latin can move words around for style, emphasis, or rhythm.

In this sentence:

• Cum tibia in atrio sonare incipit, infans ridet

the important relationships are still clear because of the forms:

• tibia = subject
• atrio = ablative after in
• incipit = finite verb of the subordinate clause
• infans = subject of the main clause
• ridet = main verb

A more English-like order would be something like:

• Cum tibia sonare incipit in atrio, infans ridet

But the original order is perfectly natural Latin.

Because Latin has no articles.

So a noun like tibia can mean:

• a flute
• the flute

and infans can mean:

• a baby
• the baby

The reader decides from context which is most natural.

This is one of the first adjustments English speakers have to make in Latin: Latin usually leaves definiteness and indefiniteness unstated unless the context makes it clear.

Infans is nominative singular, and it is the subject of ridet.

It is a third-declension noun. Its basic meaning is infant, baby, or young child.

A useful thing to notice is that third-declension nouns often do not have the neat -a / -us / -um endings that beginners may expect.

Here:

• infans = subject
• ridet = laughs / smiles

Ridet is the third person singular present active indicative of rideo.

It can mean:

• laughs
• smiles

Which English word is best depends on context.

So infans ridet could be understood as:

• the baby laughs
• the baby smiles

Both are possible translations of the same Latin verb.

Because the sentence presents the actions as happening at the same time in a general or vivid way:

• incipit = begins
• ridet = laughs / smiles

This can describe:

1. a general repeated situation

   • Whenever the flute begins to sound in the atrium, the baby laughs

2. a vivid present scene

   • When the flute begins to sound in the atrium, the baby laughs

Latin present tense, like English present tense, can do both.

In modern printed Latin, the comma is helpful because it marks the end of the cum clause before the main clause:

• Cum tibia in atrio sonare incipit, infans ridet.

It works much like English punctuation here.

However, punctuation in ancient manuscripts was much less standardized than in modern editions. So the comma is mainly an editorial aid for readers, not a fundamental part of Latin grammar.