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Both Safari and it looks like now Google Chrome as well, have a problem with playing sounds without user interaction and since the alarm is controled via timer, both browsers throw an error in the console/log and refuse to play the sound.
In Safari, this can be fixed by changing the "Settings for This Website" to allow Auto-Play. I don't know about Chrome, but I would imagine there would be some similar setting for media Auto-Play.
No issues in Firefox, other browsers not tested.