8.4 update
Alert sounds won't work for text, emails, etc. since the update. What's the fix?
iPhone 6, iOS 8.4
Open Settings and go to the Sounds section. Make sure you have sounds enabled for various types of notifications.
If this doesn't help, try to reset your device. This won't delete your data stored on the phone.
- Press and hold the Sleep/Wake button
- Press and hold on the Home button
- Keep holding both buttons until the display turns off and back on with Apple logo on it.
Alternatively, you may go to Settings - General - Reset - Reset All Settings
https://support.apple.com/en-us/HT201559
If this does not help, restore your device to factory settings. Note that this will erase the data from your device.
Take a look this Apple Support article: Use iTunes to restore your iPhone, iPad, or iPod to factory settings - Apple Support.