phone whilstles or bell rings: sounds on Samsung Galaxy S3
These are both notifications. To change them or even just find out what they are notifying you about go to Settings > My Device > Sound
You can change the "Default Notification Sound" (even choosing silent, but then you won't get any notification sounds) and a little bit lower on the menu you can set distinct defaults for specific samsung apps. There are many apps that allow you to choose different notifications sounds (other than the default that you chose above), but those have to be changed in the apps themselves. 

Do you notice any new information in the notification area (by swiping down from the top of the screen) when you hear these alerts?