Why do you need to burn a CD? Just record it and give the landlord tape. Keep a copy for yourself. Things don't have to be complicated; recording, then transfering to computer, then burning CD.

Make sure you are only recording noise that is in your apartment and nothing illegal.

I don't see how recording the noise would be useful. How would the landlord know what volume to play it back at to simulate the real situation? I could record my feet softly padding across a nice plush carpet, then ramp up the volume and make it seem like an abominable racket.