How come i can't hear sound/ alert when getting a new iPhone text message?

This is most likely due to having "Do Not Disturb" turned on. Do Not Disturb will disable all alerts when the phone is locked for the times it is scheduled to be on. Turn Do Not Disturb off by going to Settings -> Do Not Disturb -> slide to OFF.

When Do Not Disturb is enabled, calls and alerts that arrive while locked will be silenced, and a moon icon will appear in the status bar.  

Also, turn off Do Not Disturb scheduling by going to Settings -> Do Not Disturb -> Schedule -> slide to OFF.

You may also want to check to make sure your Ringer and Alerts volume is turned up.  To do so, go to Settings -> Sounds & Haptics -> then slide the Ringer and Alerts slider to the right to make the volume louder when you recieve a text message.

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I can't hear mine while Bluetooth is ON. Is your Bluetooth on?

I'll try turning Bluetooth off... I'll bet that's it. Thank you Anonymous

There is a little metal switch on the side of your phone usually above the + and - (volume). It turns on and off the ringer and it also turns on an off the sounds that alert you when you get a message or email. Switch it to "on" or towards you if you are looking at the screen. The screen will tell you know if the ringer is on. You should now be able to hear the alerts as well. Sometimes a family member or co-worker will silence a phone if it's left for a while, or you may have done it accidentally. I hoped this helps some of you.
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I can’t Hear when I getting text messages