I would like to know if it is possible to create a program using an Arduino to create an app that allows an iPhone to be notified when the door bell is rung? Ideally, it would play a chime on the iPhone or Android. This way, when I am in the basement or backyard, I would know when someone is at the door.
If it is possible, can you tell me which Arduino model I need and some sample code?
Talking to an iOS device (without Jailbreaking) with custom hardware is tough. Your best bet is to use Bluetooth 4's Low-Energy (BLE). Otherwise, you have to get a custom chip only available to certified hardware developers. Then you have to build an app and deal with the range limitations of BLE, which may or may not be a problem.
You are probably better off looking a method that connects to your home's wifi (or ethernet) and sends an email or text message.