Dear Mrs/Miss/Mz/Mr (there last name here)
I am writing this letter to say that i apologise for waking you up so early in the morning with my loud noise. I never intended to cause any harm. Please forgive me for being so inconsiderate and irresponsible. This will not happen in the future. I very much hope that we do not fall out over this as neighbours, and we can get along fine.
My sincerest apology's
(your name here)
