Lots of play in steering on rough roads mainly

I have had a wheel alignment, the tires turn fine when I turn the wheel. The problem I am having is when I hit a bump or rough roads the steering wheel shakes uncontrollably. What could this be, I have read about the steering box and gear columns. Not sure what it is. Please help. I want to buy the parts online, but I would like to have an idea of what the cause really is. The repair man that did the alignment said it would help for a bit, but to get the box replaced. Language barrier so he didn't know how to say it in English.