Why does my iPhone beep with the Messages sound at random intervals? I have an iPhone 4 running iOS 7 latest version.
Several times a day my phone will fire off the tri-tone sound and I will think I have just received an SMS, but there is nothing, and no alerts in the pull-down notifications. I have been through the list of apps in the notifications. My mail apps are in the Do Not Include section of Settings | Notification Center.

Any ideas?
In the Notification Centre settings, you can have an app only play sounds but not show any notifications, or show anything on the lock screen.

Take a look through the list for entries that only show Sound as the notification options, and turn off the sound option.