transmission "zzzzz" when it shifts
 

What is causing the transmission in my '97 XK8 to make a "zzzz" sound when it shifts.

Could be timing chain noise from the front of the engine due to weak tensioners. Mine sounded the same way at first, then progressed to making the sound whenever the engine was accelerating or shifting.

Where is the noise coming from?

Underneath you or engine compartment, left or right side or center.

Transmission fluid a bit low I suspect. pull the plug and add a 1/4 qt of Mobile 1 synthetic atf and take it for a drive. the reason the noise goes away after it warms up is the fluid expands as it get warm.

Wheeble...
mobile 1 synthetic atf is compatible with your current fluid, no worries there.

Agree w/ Wheeble, my 97 sounded like that and it was a quart low on the ATF.

Mmmmmm.... There is an additive that treats or solve transmission "whooping" during shifts (if that is your issue). Mainly a ZF tranny issue. I am not sure if it applies to 97 though... I think it started in 2004 on the Xj's. Worth investigating. Nice Car. Make sure you run nothin but synthetic in that NiKasil Engine & get those tensioners done or you may not have an engine by 100K....