yes its a common prob due to the dvd drive...

thats why im suggest you to install ur game into the HDD/thumbdrive (max space use is around 7GB per game/depends on the title). it can solved the annoying sound from the drive and also could extend ur lens life.

with the latest dashboard update it will allowed u to use a usb stick to perform as a memory device.

each slot can detect max 16GB oni.so u have 32 GB for both usb slot. only 1GB+ thumbdrive can be use as a memory device.

or

u can buy the xbox360 HDD ( 120GB or 250GB ).

how to install:
1. need to off the autoplay for disc inside the console setting.
2. insert your game disc
3. after the disc been detected press Y
4. select the option ''install game into HDD''
5. let the console saving ur game into the HDD.approx it will take around 10 min to install into the HDD.not sure how long it will take to save on the memory stick.
6. after finish installing.u can play the game as usual.

pls take note that you still have to put the game disc on for the recognition purposed.
now u will experienced game without any annoying sound from the dvd drive.