Mute should not affect music, at least not if it is playing from the Music app. It might in some third party apps, though it isn't supposed to.
Other possibilities are paired bluetooth speakers or headphones that are on, but turned down. Or, occasionally the device will decide that there is something plugged into the headphone jack, when there isn't. You can tell that because the speaker icon that shows up when you try to adjust the volume wills say headphones.