"Plötzlich habe ich das Geräusch eines Mannes gehört, der die Tür öffnete."

The versions by Sigrid sound good. You can make as well just one sentence, but it does not sound very natural. Plötzlich habe ich das Geräusch eines die Tür öffnenden Mannes gehört.

A relative sentence (or relative clause) provides extra information about a noun in the main clause and is introduced by a relative pronoun like who, which, that, or whose. It can be defining (essential to the meaning) or non-defining (extra information). Examples: 1. Defining relative clause: "The man who opened the door is my neighbor." The relative clause "who opened the door" defines which man you're talking about.

The sentence is confusing 1. What is a sound of a man? Maybe his voice? Steps? Burping? :D 2. you've heard that a sound opened the door? Because in your sentence the sound is the object doing an action. I would have said: "Plötzlich habe ich das Geräusch einer von einem Mann öffnenden Tür gehört." "Plötzlich habe ich jemanden, die Tür öffnend, gehört." "Plötzlich habe ich ein Geräusch öffnender Tür gehört."