When you are using an xbox one party to chat and use your kinect to chat you get a loud ringing sound. I have linked a video to demonstrate the sound.
To recreate this it only happens when you are in a party on xbox live, while you are in-game in destiny, and are using the kinect to chat. Others may not have this issue but 2 out of the 4 people in my xbox live party on the xbox one have been able to recreate this issue
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I found if you go to the dashboard and quit the game from there and restart it, the sound is fixed. But i am not sure what triggers it to happen. seems random, it started for me right after leaving the level 24 strike mission. Every time it happens i just dashboard, press menu and quit game. and restart.