Samsung Galaxy Core - How to turn off notification tone throughout text conversation?

[cherylmcc]

On my Samsung Galaxy Core 4G - When texting back & forth, the other person's reply is always accompanied by a notification tone. I only want to be notified when the text message first comes in. How can I turn off being notified everytime the other person replies throughout our conversation. Help and thank you.

 

[cherylmcc]

Thank you for your reply, but I don't want to block the sender. I just don't want the notification tone to repeat with every reply during a conversation.