Some people who use iOS 9 report that there some troubles at notification sounds for incoming messages in their phones. It works normally for some messaging apps but it does not work for other messaging apps and there is no sound when there is incoming message.
This condition is quite disturbing because when it comes to important messages, it needs more effort to know whether the message is already received by the phone or not. Of course you do not want to miss those important messages and do not read them on time just because there are no notification sounds of them.
To overcome this problem, you can try to turn the Volume up as you ensure that no notification sound at your incoming message is not because your low phone Volume. You also have to check whether the Mute switch in your phone is on or not. If the Mute is on, you have to switch it off.
You also can try these steps: take a look under Settings then choose Do Not Disturb. Or please try these steps: tap Settings, then choose Notifications and toggling them on or off and reboot your device then please turn them on again.
It is possible that your phone setting is related to your no notification sounds issue. Try to reset your iOS 9 setting by following these steps: tap the Settings, then tap General, and choose Reset, then Reset All Settings. You must be aware that you have to re-enter all of your settings to your device after this action.
If your iOS 9 no notification sounds problem is because your Siri is muted, you can directly go to Settings, then tap General, then choose Accesibility, then tap Voice Over, then Speech, and choose Default Dialect then choose one according to your preference and your phone will back to normal as you also ensure that your Mute switch is off.