Three posts in 17 minutes with the 2nd only 8 minutes after your first post. Time to chill. There are not a bunch of users waiting here to answer questions.
There are questions that need answers before someone can answer the correct solution. First, how old is your MBA? Does it have a DVI or HDMI output? I'm not sure what you mean by HDMI converter. My previous MB had a DVI out so I had to get my sound via a 3.5mm audio cable from the 3.5mm jack (headset jack).
Due to restriction, there are some output videos that only port over either the sound or the video.
Your machine has one of two video output ports:
1.) Micro DVI
2.) MiniDisplay Port*
*Technically it's called a Thunderbolt now but it uses MiniDisplay Port adapters so we'll stick with that naming convention until Thunderbolt to DVI/HDMI adapters come out.
What ports do you have on the back/side/front of your TV: DVI, HDMI, Component, Composite, S-Video? Secondly what exactly did you buy? What is the manufacturer/brand and model of this "HDMI converter" you purchased?
If you have a newer MacBook Air (less than 2 years old) and your TV supports audio & video from a computer source over HDMI then this adapter would work to accomplish your task -
Otherwise you'll need to provide more information about the equipment and MacBook Air you're working with for anyone to be of meaningful assistance.