There should be no sound from text messages when you turn on the phone's quiet / vibrate mode, and the only notice you'll get is a vibration. Because the SMS notice continues to ring, the problem might be due to a software error. To force a restart, press and hold the Sleep/Wake and Volume Down buttons simultaneously for at least 10 seconds, then release the buttons when you see the Apple logo. Check to see whether the problem persists after completing this step. If that's the case, double-check your phone's settings. If the volume is turned down to the bare minimum? Is the vibrate/silent switch turned on? Whether nothing appears to be incorrect with the phone's settings, you should see if there is a software update available and install it. There is one more troubleshooting step that you should think about. r is to backup your phone data then restore the phone and set it up as a new device.