Just carefully STOP one fan at a time when the buzzing occurs. You can do it manually by pressing in the CENTER of the fan if careful, or better open the FAN SOFTWARE and stop the fan if possible when it's buzzing.
PSU and HDD?
The PSU would obviously work harder to supply power to the parts, thus the fan can spin harder, but the hard drive won't. It will just load the program into main system memory. Usually an HDD noise is pretty obvious, and you can touch the drive itself to dampen resonance if you suspect it.
CPU fan?
Possibly, though it's pretty hard to cause case resonance.
Having said that, stock fans can get pretty loud so you may wish to investigate a better cooler like:
a) $25 or so -> Cooler Master ... "EVO" (see pcpartpicker)
b) $63 of so -> Noctua NH-U12S
The Noctua is a lot more money but also SILENT most of the time if setup properly in fan control software (preferably from motherboard support site).
Summary:
*I'm pretty sure it's a CASE FAN, which again you can test by stopping when it's buzzing as suggested.
My dad's front fan would suddenly cause the case to be horribly loud. I ended up just removing it since it turned out it wasn't really needed. My dad has an i5-4670K, no graphics card, and the case temperatures never go above 40degC. I could have cooled the hard drive slightly but it's temps are fine so I just unplugged the fan since I'd have to go back and fix it if it started up again...
If so, you can google for information on reducing noise, but basically find a thin material you can place in between the fan and case to dampen noise. Sometimes a few pieces of folded, thin cardboard can help if jammed in or look for some rubber, plastic, gasket, whatever.