Sometimes music will not play loudly when using the iPod app on your iPhone. There could be several reasons for this, but one to check is the built-in volume limit setting. The volume limit sets a maximum volume to be output on the speaker or headphone jack, limiting the top volume that can be set using the side volume buttons.
To increase the volume limit on the iPhone:
1. Navigate to Settings -> iPod
2. Check the Volume Limit.
3. If the Volume Limit is OFF the volume is maxed out.
4. When the Volume Limit says ON there is a limit set.