Mine trådløse hovedtelefoner ligger ved siden af computeren på skrivebordet.

Because hovedtelefoner is plural.

Danish possessive forms change like this:

• min
  • singular en-word
• mit
  • singular et-word
• mine
  • plural nouns

So:

• min computer
• mit skrivebord
• mine hovedtelefoner

Since hovedtelefoner is plural, mine is the correct form.

The adjective trådløs changes form depending on grammar.

Basic pattern:

• trådløs for many singular en-words in indefinite phrases
• trådløst for singular et-words
• trådløse for plural, and also in definite/possessive-type phrases

Examples:

• en trådløs mus
• et trådløst headset
• mine trådløse hovedtelefoner

So in this sentence, trådløse is the expected form.

Because after a possessive such as min, mit, or mine, Danish normally uses the noun without the definite ending.

So:

• my headphones = mine hovedtelefoner
• not mine hovedtelefonerne

This is different from English, where you already use a separate word like the. In Danish, definiteness is often built into the noun itself, but after a possessive, you do not add that definite ending.

Because Danish often treats headphones the same way English does: as a plural noun when talking about the whole item.

So hovedtelefoner is the normal word for headphones as an object you own or use.

If you want to talk about one side/piece, you can say en hovedtelefon.
If you want to emphasize the whole pair or set, you can also say et sæt hovedtelefoner.

Danish often prefers a position verb when describing where something is located.

Common ones are:

• ligger = lies, is lying
• står = stands, is standing
• sidder = sits, is attached/positioned
• hænger = hangs

For headphones placed on a desk, Danish naturally uses ligger, because they are understood as lying there.

So Mine trådløse hovedtelefoner ligger ... sounds more natural than just using er.

You can sometimes use er in broader location statements, but ligger is the idiomatic choice here.

Ved siden af is a fixed expression meaning next to or beside.

Yes, you normally need the whole expression.

Structure:

• ved siden af + noun

Example:

• ved siden af computeren = next to the computer

Literally, it is something like at the side of, but you should learn it as one set phrase.

Because Danish usually marks definiteness by adding an ending to the noun.

Here:

• en computer → computeren = the computer
• et skrivebord → skrivebordet = the desk

So the endings work like English the.

Also notice the genders:

• computer is an en-word
• skrivebord is an et-word

That is why the endings are different:

• -en for many en-words
• -et for many et-words

In normal understanding, the sentence means that the headphones are located on the desk, and they are next to the computer.

So the most natural reading is:

• the headphones are on the desk
• the computer is there too
• the headphones are beside the computer

Like English, Danish can sometimes allow slight ambiguity in longer location phrases, but in everyday use this sentence is understood naturally without a problem.

Yes. Danish main clauses follow the verb-second rule, so different word orders are possible as long as the finite verb stays in second position.

For example, you can say:

• Mine trådløse hovedtelefoner ligger ved siden af computeren på skrivebordet.
• På skrivebordet ligger mine trådløse hovedtelefoner ved siden af computeren.

Both are grammatical. The second version puts more emphasis on på skrivebordet.

This is a very common Danish pattern: if you move a time/place phrase to the front, the verb still has to come right after it.

Yes, people would understand it, but ligger is more natural.

Using er gives a more general statement of location. Using ligger sounds more idiomatic because Danish likes to describe the physical position of objects.

So:

• er = understandable
• ligger = more native-like here

If you want to sound natural in Danish, choosing the right position verb is very useful.