Light fixture emits a high pitch sound with no bulb
The noise is coming from the ballast (the part which converts 120 or 240 (or whatever the local standard is) VAC to the voltage and current required for the fluorescent bulb. Given that the fixture no longer works with a new bulb, that has failed, but some portion of it is still trying to work and the high-speed electrical switching common in newer-style ballasts is making the noise.

Best bet would be to replace that ballast (they do not live forever) so the light is useful again. Or, as suggested by @John, you could remove the power to the ballast (and remove the entire fixture, if you don't plan to fix it - a cover plate would go on the ceiling electrical junction box.) A third option would be to have the light retrofitted to an LED type fixture (which uses a different "ballast" or power supply) or replace the entire fixture.