Soundproofing a back door.

[Jon Held]

Hello.  I have a question about soundproofing.

My apartment has a back door, with an air-conditioner on top and a thin wall 
up to the high ceiling (2 layers of plywood).  There is a loud exhaust fan 
>From a restaurant near my back door.  The sound (mostly mid-range whines) 
comes through my backdoor and thin wall and skylight, and it is quite loud 
>From within my apt.  

I would like to cover the outside of the back door, and especially the wall 
over it, with something, to shield more sound.  

Which shields (midrange) sound better - wood or styrofoam?

Any other advice about making the apt more quiet is appreciated.

Thank you!

-Jon Held