Afgangen er forsinket, så vi venter i ventesalen.

It marks the noun as definite singular: afgangen = the departure.

The basic noun is:

• en afgang = a departure

When Danish wants to say the departure, it usually adds the article to the end of the noun:

• afgang → afgangen

This is very common in Danish.

Because Danish normally puts the onto the end of the noun instead of using a separate word in front.

So:

• en afgang = a departure
• afgangen = the departure
• en ventesal = a waiting room / waiting hall
• ventesalen = the waiting room

A separate definite word such as den is used in other situations, especially when there is an adjective:

• den forsinkede afgang = the delayed departure

Forsinket is the past participle of at forsinke and is used like an adjective here.

So:

• at forsinke = to delay
• forsinket = delayed

In the sentence:

• Afgangen er forsinket

it means The departure is delayed.

So er forsinket works like is delayed in English.

Because så here is being used as a coordinating conjunction meaning so.

When så connects two main clauses, the second clause keeps normal word order:

• så vi venter

That is:

• så
  • subject
    • verb

If you used a word like derfor instead, then Danish would normally invert the order:

• Afgangen er forsinket. Derfor venter vi i ventesalen.

So this sentence is correct as written.

It means so here, in the sense of therefore / as a result.

The logic is:

• The departure is delayed, so we wait in the waiting room.

It does not mean because in this sentence.

Compare:

• Afgangen er forsinket, så vi venter i ventesalen.
  Result: the delay leads to the waiting.

• Vi venter i ventesalen, fordi afgangen er forsinket.
  Reason: we are waiting because the departure is delayed.

So så gives the result, while fordi gives the reason.

Because Danish does not have a special progressive form like English am waiting / are waiting.

Danish simply uses the present tense:

• vi venter

This can mean:

• we wait
• we are waiting

The context tells you which meaning is intended.

Also, Danish present tense is easy:

• jeg venter
• du venter
• vi venter

The verb form does not change for different persons.

Because vente can be used without an object when you simply mean to wait.

Here the sentence only says where the people are waiting:

• vi venter i ventesalen

If you want to say what they are waiting for, then you usually use på:

• Vi venter på toget. = We are waiting for the train.
• Vi venter på afgangen. = We are waiting for the departure.

So in your sentence, på is not needed.

Because i is used for being inside an enclosed space.

So:

• i ventesalen = in the waiting room

That is the natural preposition here.

Danish often uses:

• i for something inside a room, building, city, box, etc.
• på for surfaces, islands, some institutions, events, or certain set expressions

Since a waiting room is an indoor space, i is the normal choice.

It is a compound noun, which is very common in Danish.

You can break it down like this:

• vente = wait
• sal = hall / room
• -en = the

So:

• ventesal = waiting hall / waiting room
• ventesalen = the waiting room

In Danish, compounds are usually written as one word, not two.

In travel language, afgang usually refers to a departure or a scheduled service/departure time.

Depending on context, it could be a:

• train departure
• bus departure
• flight departure
• ferry departure

So afgangen er forsinket does not necessarily focus on the physical vehicle itself. It often means that the scheduled departure is delayed.

Because the sentence contains two full clauses:

• Afgangen er forsinket
• vi venter i ventesalen

The comma separates them clearly, and this is very common in Danish writing when two independent clauses are linked by a conjunction like så.

So the comma helps show the structure:

• first clause: the situation
• second clause: the result