Engine fan is known as Viscose clutch fan that have silicone padding inside and once engine heats up that silicone expands and engine fan work at higher speed (same as engine rpm).
Usually engine fan works at half speed of engine due to viscose padding holding it tight inside and when viscose fluid expands (due to overheating) and make engine fan free than it rotate at full speed causing this high pitch noises. Check the fan and rotate it while car is off, if its moving freely then viscose fluid is bad and you need new fan clucth there. If it rotate with little resistance and stop immediately after turning by hand then it means its fine.
Check that and let us know, so that we can help you further. Good luck.