Sound even with the use of mini displayport?

Hello guys. I want to connect my PS4 to my MacBook Air 13". Thus I was wondering if it's worth getting a mini displayport to HDMI adapter for my MacBook Air 13". I'm not sure, because I don't know if I will get sound (out of the MacBook) from my PS4, even though I'm using the mini displayport to connect the two. Has anyone got an idea whether this would work or not?
Thanks in advance.