How can I sound proof sliding glass doors that face a LOUD freeway?

I just moved into this apartment, and it is very nice with one major exception. The bedroom has sliding glass doors which face a very loud freeway, and It sounds like the thing is open all the time. I thought I would get used to the noise, but after a couple of weeks, I am still loosing sleep. I went to Lowes and Home Depot and even a music shop, but no one had any real solution. The hardware stores suggested I purchase these 8×4 foot (2/3″ thick) insulation boards and then cut them to size to “plug” the doorway. This is not a problem, because I don’t need to go in and out of this door, however, I am not sure that these panels will be enough. I am hoping someone has run into a similar problem and found a solution. The only other option is to wear ear plugs, which I did last night, but then you have to deal with not hearing anything (which is almost as bad as hearing everything if you know what I mean). Thanks in advance for your suggestions.