Is there a method that can be used to mute the global sound from an application button?
They make it more complicated than it has to be. You can just use AudioManager.setStreamMute(). Feel free to use the code below.
//mute audio
AudioManager amanager=(AudioManager)getSystemService(Context.AUDIO_SERVICE);
amanager.setStreamMute(AudioManager.STREAM_NOTIFICATION, true);
amanager.setStreamMute(AudioManager.STREAM_ALARM, true);
amanager.setStreamMute(AudioManager.STREAM_MUSIC, true);
amanager.setStreamMute(AudioManager.STREAM_RING, true);
amanager.setStreamMute(AudioManager.STREAM_SYSTEM, true);
//unmute audio
AudioManager amanager=(AudioManager)getSystemService(Context.AUDIO_SERVICE);
amanager.setStreamMute(AudioManager.STREAM_NOTIFICATION, false);
amanager.setStreamMute(AudioManager.STREAM_ALARM, false);
amanager.setStreamMute(AudioManager.STREAM_MUSIC, false);
amanager.setStreamMute(AudioManager.STREAM_RING, false);
amanager.setStreamMute(AudioManager.STREAM_SYSTEM, false);