Hi,
The timing belt isn't the likely cause of the noise. However, the serpentine belt is.
Based on your description, it sounds like there is a problem with the idle air control valve (IAC). The IAC is responsible for maintaining engine idle speed. Here is what I suggest: The first thing I would do is check for engine vacuum leaks. Here is a link that explains how that is done:
https://www.2carpros.com/articles/how-to-use-an-engine-vacuum-gauge
If none are found, next is to remove the IAC, inspect it for carbon build-up/dirt, and clean it and the airway it plugs into. The IAC is located on the throttle body. I will need to know the specific engine you have and if it is turbocharged to get specific information, so let me know.
We do have a procedure for servicing the IAC, but based on the engine, it may be recommended to avoid cleaning.
Let me know if you find leaks and the engine size.
Joe
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Thursday, November 4th, 2021 AT 8:43 PM