It's actually quite unlikely you could hear a hard disk starting and stopping above the noise that fans commonly make.
So my suggestion is that maybe you can haer a fan starting and stopping. On a laptop this happens all the time - on a destop it normally wouldn't happen (unless you have thermostatic fans, which is unusual.
So I would recommend you to look carefully inside the system, to see if in fact you can see a fan stopping and starting.
If it really is the hard drive, then put a different power connector into it - perhaps the one you are using is faulty.
Secondly look in the power settings and see if the hard drive is set to turn off quickly (it shouldn't be - unless it's a laptop,