I've had this happen on both my XBOnes. Both these solutions have worked for me.
#1 Solution
In Destiny press the Xbox Home Button (brings up home screen)
Press the Show Menu button (one with 3 lines on it)
In the menu that comes up select Quit
#2 Solution
If #1 doesn't work this has always worked for me. Turn off Box and pull the power plug.
Near as I can tell this is a sleep/wake problem. When you shutdown the One really doesn't shut off but goes to sleep/hibernation. When it wakes back up the Destiny sound process doesn't come back with it. In order to restore sound Destiny needs to be rebooted.
English
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Solution 1 worked for me. Thank you.
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Or u can press home button then go back to destiny again
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For some reason that doesn't work for me. I haven't tried since this weeks patch. In the habit now of quitting Destiny when I log off.