Tvivlen forsvinder, når læreren forklarer det roligt.

Tvivl means doubt.

Tvivlen is the definite singular form, so it means the doubt.

In Danish, the definite article is usually added to the end of the noun:

• en tvivl = a doubt
• tvivlen = the doubt

So Tvivlen forsvinder means The doubt disappears.

Forsvinder is the present tense of forsvinde = to disappear.

A lot of Danish present-tense verbs end in -r:

• forsvinde → forsvinder
• forklare → forklarer

Here, the present tense is used for a general situation or something that typically happens: when the teacher explains it calmly, the doubt disappears.

Here når means when.

It introduces a time clause: when the teacher explains it calmly.

A useful comparison:

• når = when (general, repeated, or future)
• da = when (about a specific event in the past)
• hvis = if

So in this sentence, når is used because the meaning is general: whenever the teacher explains it calmly, the doubt disappears.

Læreren means the teacher.

It is the definite form of en lærer = a teacher.

• en lærer = a teacher
• læreren = the teacher

Danish often uses the definite form when the person is understood from the situation or context. So this sentence is talking about the teacher as the relevant teacher in that situation, not just any teacher.

Det means it here.

It refers to whatever the teacher is explaining — an idea, a problem, a point, or the thing causing doubt.

Danish often uses det for:

• abstract things
• whole ideas
• situations
• something already understood from context

Why not den?

• den usually refers back to a specific common-gender noun
• det often refers to something more neutral or abstract

So forklarer det is a very natural way to say explains it.

Because roligt is being used adverbially here.

The adjective is:

• rolig = calm

But when it describes how someone does something, Danish often uses the -t form:

• rolig = calm
• roligt = calmly / in a calm way

So:

• en rolig lærer = a calm teacher
• læreren forklarer det roligt = the teacher explains it calmly

The sentence has:

1. a main clause: Tvivlen forsvinder
2. a subordinate clause introduced by når: når læreren forklarer det roligt

In the main clause, Danish normally follows verb-second word order, so the finite verb comes early:

• Tvivlen forsvinder

In the subordinate clause, the word order is more like English:

• når læreren forklarer det roligt
• subject læreren comes before the verb forklarer

You can also put the når clause first:

• Når læreren forklarer det roligt, forsvinder tvivlen.

That is also correct, but then the main clause begins with the verb forsvinder.

Usually roligt here is best understood as calmly, gently, or in an unhurried way.

It does not necessarily mean the teacher is speaking softly. It is more about the teacher’s manner being calm and steady.

So forklarer det roligt suggests that the explanation is clear and not rushed or agitated.

The comma separates the main clause from the subordinate clause.

So:

• Tvivlen forsvinder = main clause
• når læreren forklarer det roligt = subordinate clause

In Danish, you may see a comma before a subordinate clause like this. This is called start comma. It is common and correct.

You may also see Danish written without that comma, depending on the comma system being used. So both of these can occur:

• Tvivlen forsvinder, når læreren forklarer det roligt.
• Tvivlen forsvinder når læreren forklarer det roligt.

The version with the comma is very common in teaching materials because it makes the clause structure easy to see.