U asked the question by starting to give us bad information. The above model is a sound system, nothing to do with youtube unless you are interested in "listening" to youtubes only.
Read your TV manual, it may have a youtube widget, if it's a smart TV at all, then you can play directly from the TV without an iPhone. If not, you have to purchase an AppleTV box $99, hook that up to the TV, THEN u can have iPhone talk to that box with AirPlay, wirelessly. This only works for iPhone4s and 5, again you did not specify which phone model you have.