I found the problem. The iPhone thinks it is sending the sounds through the Dock Connector. Why it is doing this I am not certain, but to fix it I plugged my iPhone into my Mac and the sounds were back immediately. I then ejected it from iTunes and the sounds are working fine. This must have reset the software so it now plays the sounds through the iPhone's speakers instead of the Dock.
I this might have been caused be caused I used the USB port on my car to charge the phone. That might have also caused the iPhone to think it was connected to a Dock and somehow that never got reset when I disconnected the iPhone.
Apple should know this because the solution is very simple.