Du behøver ikke at tale så højt; der er allerede nok støj i rummet.

Behøver means need or have to, so Du behøver ikke at tale så højt means You don’t need to speak so loudly.

This is different from simply negating tale:

• Du taler ikke så højt = You are not speaking that loudly
• Du behøver ikke at tale så højt = You don’t need to speak that loudly

So behøver ikke expresses lack of necessity, not just simple negation.

Also, Danish often uses behøve in negative sentences:

• Du behøver ikke komme = You don’t need to come
• Jeg behøver ikke vente = I don’t need to wait

Yes, at can often be left out after behøver in everyday Danish.

So both are possible:

• Du behøver ikke at tale så højt
• Du behøver ikke tale så højt

Both are natural. The version with at can sound a little more careful or formal in writing, but neither is strange.

This is similar to English having both:

• You don’t need to speak
• You don’t need to be speaking
  Not exactly the same structure, but the idea is that small function words may be included or omitted depending on style.

Because højt is the adverb form here.

• høj = high/loud as an adjective
• højt = loudly / in a loud way as an adverb

In this sentence, højt describes the verb tale (to speak), so Danish uses the -t form:

• Han er høj = He is tall
• Musikken er høj = The music is loud
• Han taler højt = He speaks loudly

So in tale så højt, højt means loudly, not loud.

In this sentence, så højt means so loudly.

This is the natural Danish choice in this kind of statement:

• Du behøver ikke at tale så højt = You don’t need to speak so loudly

Så often corresponds to English so:

• Det er så dyrt = It is so expensive
• Hvorfor råber du så højt? = Why are you shouting so loudly?

Meget højt means very loudly, which is possible in some contexts, but it is not as natural here:

• Du taler meget højt = You speak very loudly

So:

• så højt = the usual phrase in this sentence
• meget højt = more like a straightforward degree statement, very loudly

Der er is the normal Danish way to say there is / there are.

So:

• der er allerede nok støj i rummet = there is already enough noise in the room

Here, der does not mean there in the sense of location. It is a grammatical placeholder, just like English there in:

• There is a problem
• There are many people here

Compare:

• Bogen er der = The book is there
  Here der really means a place.
• Der er en bog på bordet = There is a book on the table
  Here der is just the existential there.

Allerede means already.

It emphasizes that the room has enough noise as it is, so more loud speaking is unnecessary:

• der er nok støj i rummet = there is enough noise in the room
• der er allerede nok støj i rummet = there is already enough noise in the room

So allerede strengthens the idea: the room is noisy now; we do not need more noise.

No, not here.

In this sentence, nok means enough:

• nok støj = enough noise

Danish nok can mean different things depending on context:

1. enough

   • Der er nok mad = There is enough food

2. probably / I suppose / likely

   • Han kommer nok senere = He’ll probably come later

In der er allerede nok støj i rummet, it clearly means enough, because it comes before a noun: nok støj.

Because støj is usually an uncountable noun, like noise in English.

So Danish says:

• nok støj = enough noise

You normally do not count it as separate units. This works much like English:

• There is too much noise
• not usually There are many noises unless you mean different distinct sounds

So støj here behaves like a mass noun, not a count noun.

Because i means in, and with rooms/enclosed spaces Danish normally uses i:

• i rummet = in the room
• i huset = in the house
• i bilen = in the car

På usually means on, or is used with certain locations by convention:

• på bordet = on the table
• på skolen = at the school
• på hospitalet = in/at the hospital in some uses

But for a physical room, i rummet is the normal choice.

The basic word order is very typical Danish main-clause word order:

• Du = subject
• behøver = finite verb
• ikke = negation
• at tale så højt = infinitive phrase

So the structure is: Subject + finite verb + ikke + infinitive

This is common with modal-like verbs and similar constructions:

• Jeg kan ikke komme = I can’t come
• Vi vil ikke gå = We don’t want to go
• Du behøver ikke at tale så højt = You don’t need to speak so loudly

The important thing for learners is that ikke usually comes after the finite verb in a main clause.

Yes. The semicolon is a punctuation choice, not a grammar requirement.

You could also write:

• Du behøver ikke at tale så højt. Der er allerede nok støj i rummet.
• Du behøver ikke at tale så højt, der er allerede nok støj i rummet.
  Though this comma version is less ideal in careful writing.

The semicolon works well because the two clauses are closely related:

1. You don’t need to speak so loudly
2. There is already enough noise in the room

So the semicolon links two complete thoughts that belong together.

Yes, du is the normal singular you, and in modern Danish it is used in most situations, including many that would be formal in some other languages.

There is also De as a formal you, but it is now quite rare and mostly used in very formal, old-fashioned, or special service situations.

So in normal modern Danish, Du behøver ikke at tale så højt is exactly what you would expect.

Yes, definitely.

You could say:

• Du behøver ikke at snakke så højt

This means almost the same thing.

Very roughly:

• tale = speak
• snakke = talk

But in everyday Danish, snakke is extremely common and natural. Tale can sound a little more neutral or slightly more formal depending on context.

So both work well here:

• tale så højt
• snakke så højt

It is softer than a direct command.

• Tal ikke så højt! = Don’t speak so loudly!
  This is a direct imperative.
• Du behøver ikke at tale så højt = You don’t need to speak so loudly
  This sounds less harsh and more indirect.

So the sentence is still telling someone to lower their voice, but in a milder, more polite way. The second clause, der er allerede nok støj i rummet, gives a reason, which also makes it sound less abrupt.