How to Turn Off Ringtones on an Apple iPhone
While silencing your Apple iPhone using the "Ring/Silent" switch on the left side of the device will turn off all ringtones, it will also not play alerts or sound effects. This will keep you from hearing notification sounds associated with applications like "Messages" and "Mail." To turn off your iPhone's ringer, but keep other notifications enabled, you will need to adjust your Sound settings.
Tap the "Settings" icon from your home screen.
Tap the "Sounds" tab.
Drag the slider under the "Ring" section all the way to the left.