Exhaust replacement

[banpei]

I think I found a possible reason why my Tanabe exhaust is louder than it should be. I found a sales advertisement for the same Tanabe Hyper Medalion exhaust on a Russian site. This is a picture of the exhaust tip:


And this is a picture of my exhaust tip:


I've seen a similar thing on some of the other Japanese performance exhausts there is a funnel-shaped part that you can take out of the exhaust tip. For example, this Tanabe exhaust has such a funnel:

So I'm wondering that if my car is missing this funnel, could that be the reason why it's extremely loud? Or is it actually the other way around and the funnel bypasses the second silencer?