Receiving an Unknown iOS Notification -- Audio Only
Yes, you can, you just have to do some digging around to find the particular one that is causing the noise. If you go into your Settings application on your iDevice, and go into the Notifications Options Tab and look for apps that have the sounds attribute available.  As seen the in the screen shot below highlighted in red.  



Selecting that one will take you further into the customizations and see if the app is sending other notifications, as shown below, this one does sound and badge and can be seen in the lock screen.  Toggling those on and off will help you find the culprit.



You will be looking for an App that is only making noise, look for one that says noise only and everything else is turned off, that one will most likely be the problem.  You can then turn on other notifications so that it will be more helpful. If you find more than one app that is noise only, enable more notification types to help you narrow down which one it is. Once you find it, you can disable it or change the setting any which way you want.

I hope that this answer helps you narrow down the noisy notifier.