gotta be sure we're talking abou the same thing at the same time, here - this...
... Is when you hear the pop? Or is it more of a grinding noise? If it's grinding, and happening while you're backing up with the wheel at full lock, i suspect your steering stop caps have worn off and are grinding on eachother. A quick dab of multipurpose grease will shut them up. If it's happening after full lock, as you're straightening out and pulling forward, it's probably a cv shaft. Your mechanic should be able to inspect the shafts and tell you for sure if that's what is causing the trouble before he charges you to replace them.
Then you get this when you're accelerating from a dead stop, and it doesn't matter whether you're turning or going straight, right? Could be a lot of things, do you feel it in the steering wheel? Or is it more of a whole body shake?