Do all Cinema Displays emit noise at reduced/minimum brightness?
It is not normal for the aluminum or polycarbonate cinema displays to make audible noise. They have been used 24x7 for a decade in recording studios and 3D and production cutting rooms where we put the CPU in a sound isolating box and never had to mitigate a Cinema Display due to noise until they start to fail. Many of these places are very low light so brightness is often way below max for us. 

When the power transformer starts to fail, that can then make the display make noise and these displays and power bricks were manufactured in pairs so swapping power supplies from two working pairs would make both get noisy. Don’t just assume the part that makes noise is the culprit. 

Like Allan and bmike have said there is something wrong with your display when driven by the adapter that supplies the transformed power from mains. 

If you have to hit something to make it behave properly... Well an Apple Cinema display is not a mid 60s-era color TV and that should not happen.

You can do two things


Replace it
Have it repaired


Repair could be conditioning or filtering the mains power so the Apple power supply does less work and filtering. 
Locate a new power supply that makes your display quiet again. 
Have the LCD panel disassembled and inspected. If physical hits and taps alter vibration, it might just be a failed internal physical mount that needs repair. 



I would imagine that #2 might cost more than the value of a replacement unless you’re unable to source a matte LCD panel of that size.