Constant dinging would drive me bananas! I can definitely understand wanting this sound to go away! Let's get this fixed for you, right away.
Software updates do often reset default settings for your phone. This can cause notifications to sound that may have been previouly turned off.
Check the sounds in your Sounds Menu. Access 'Settings' then 'Sounds'. Here you are able to view all the controlled sounds for your iPhone's native (pre-installed) applications.
Sounds for Apps you have installed are controlled in Notifications. If you go to 'Settings' then 'Notifications' you can see which apps are configured to give a sound. You may have to go through each application listed and turn them off in a process of elimination.
I am confident these steps will lead you to the cause of the constant ding.
Please let me know if you need further assistance. I'm here to help.
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