Laptop buzzing (not HDD, not fan). How to hush it?

As noise is connected to the load (and thus current consumption) this might be case of noisy DC-to-DC converter whose switching frequency falls into audible range.

It is hard to tell whether it is serious or not but I would definitely look into replacing the laptop if it is in warranty as big shift in DC-to-DC switching frequency quite often can have impact on voltages it generates. Even if currently it works fine, long-term you might find some of more sensitive components just dropping dead one-by-one.

I think I had the same problem a while ago. When the CPUis working at full speed it is silent, but when the workload is lower the CPU goes into power-saving mode. That is when it starts making noise. My problem was solved by switching off D-states in BIOS. Amazingly neither the computer support at our company nor the two engines DELL sent out to fix the noise could solve my problem. Luckily I found the answer on internet...