La muziko sonas tiel laŭte, ke la infano ne povas dormi.

La is the definite article, meaning the.

In this sentence, la muziko means the music and la infano means the child. That usually suggests the speaker has a specific music source and a specific child in mind, or that both are already known from context.

Esperanto has no indefinite article. So:

• infano = a child / child
• la infano = the child

Without la, the sentence would feel less specific.

Sonas comes from soni, meaning to sound.

So:

• La muziko sonas laŭte = The music sounds loudly / sounds loud
• La muziko estas laŭta = The music is loud

These are very close in meaning here.
Using sonas focuses a bit more on how the music is perceived by hearing.

A useful pattern is:

• ĝi estas bona = it is good
• ĝi sonas bone = it sounds good

So soni often pairs naturally with an adverb.

Because laŭte is an adverb, and it describes how the music sounds.

In Esperanto:

• -a = adjective
• -e = adverb

So:

• laŭta muziko = loud music
  (laŭta describes the noun muziko)
• La muziko sonas laŭte = The music sounds loudly / loud
  (laŭte describes the verb sonas)

This is a very common pattern after verbs like soni, aspekti, and sentiĝi.

Tiel ... ke means so ... that.

It introduces a result:

• tiel laŭte = so loudly
• ke la infano ne povas dormi = that the child cannot sleep

So the structure is:

tiel + adverb/adjective + ke + result

Examples:

• Li estas tiel laca, ke li ne povas labori.
  He is so tired that he cannot work.
• Ŝi parolas tiel rapide, ke mi ne komprenas.
  She speaks so quickly that I do not understand.

Yes, but the meaning changes slightly.

• tiel laŭte, ke ... = so loudly that ...
  This simply states the degree and its result.
• tro laŭte = too loudly
  This adds the idea of excess or more than is acceptable/desirable.

So:

• La muziko sonas tiel laŭte, ke la infano ne povas dormi.
  = The music is so loud that the child cannot sleep.
• La muziko sonas tro laŭte por ke la infano dormu.
  = The music is too loud for the child to sleep.

Both are natural, but they are not exactly the same construction.

Ke is a conjunction meaning that.

Here it introduces the clause showing the result of the music being so loud:

• La muziko sonas tiel laŭte
• ke la infano ne povas dormi

So ke connects the first idea with what happens because of it.

Esperanto uses ke very often for subordinate clauses:

• Mi scias, ke li venos. = I know that he will come.
• Estas tiel varme, ke mi ne povas labori. = It is so hot that I cannot work.

After povi (can / be able to), Esperanto uses the infinitive of the main verb.

So:

• povas dormi = can sleep
• ne povas dormi = cannot sleep

This is just like English:

• The child can sleep
• The child cannot sleep

You do not conjugate the second verb:

• correct: povas dormi
• not correct: povas dormas

In Esperanto, ne usually goes directly before the word it negates.

So:

• la infano ne povas dormi = the child cannot sleep

Here, ne negates povas, so the meaning is that the child is not able to sleep.

Compare:

• La infano povas ne dormi.
  = The child can choose not to sleep / may not sleep.

That is a different meaning.
So the position of ne matters.

Esperanto word order is fairly flexible, but the standard order here is the clearest and most natural.

Normal order:

La muziko sonas tiel laŭte, ke la infano ne povas dormi.

You could rearrange parts for emphasis, but beginners should usually keep the standard order.

For example, Tiel laŭte sonas la muziko... is possible, but it sounds more marked or literary.
The ordinary version is best for everyday use.

Laŭte is pronounced roughly like LOW-teh.

A few details:

• aŭ is a diphthong, like ow in cow
• e is pronounced like eh
• stress in Esperanto is always on the second-to-last syllable

So:

• laŭ-te
• stress on laŭ

That gives LOW-teh.

This is a very common learner question.

In Esperanto, after verbs like soni (to sound), using an adverb is very natural:

• Ĝi sonas bone. = It sounds good.
• La muziko sonas laŭte. = The music sounds loud/loudly.

English often uses an adjective after sound, but Esperanto commonly uses the adverb because it describes the manner of sounding.

That said, learners may sometimes encounter adjective-like logic in other contexts, but for this sentence, laŭte is the expected form.

No, that would not be normal Esperanto.

If you want the so ... that idea, you need tiel ... ke.

So this is correct:

• La muziko sonas tiel laŭte, ke la infano ne povas dormi.

Without tiel, the sentence sounds incomplete because ke needs that setup.

If you do not want the result construction, you could instead say something like:

• La muziko sonas laŭte. La infano ne povas dormi.

But then you just have two separate statements, not the connected so ... that structure.