Measuring TT Speed

Reality check: no belt, motor, AC, or anything else gonna make the lines "bounce back and forth" the changes in platter speed for that to happen are just insane, beyond the torque of the motor, and the OP wouldn't even need a strobe the table would be totally unlistenable. 

Its just light hitting the strobe bars at the wrong time. Ignore those, concentrate on the average, you'll be fine.

I am using the KAB light and disc for those interested...

Lewm, as far as I can tell the RPM app works great. I have a record weight with a flat top so I just put the phone on top of that. The phone reports in hundredths of a revolution. When I first tried it the phone reported a wow and flutter of 1.78 % which sucks. I got a new belt and wow and flutter dropped to 0.07%....on a 40 year old turntable. 
For speed it is certainly more accurate than a strobe. If I adjust it with the phone to an exact 33.33 RPM the strobe is dead still. It is cheap. I suggest you try it and tell us what you think! 

On the other hand, if you can't adjust your turntables speed it might piss you off.

jsman, if you're using the KAB strobe light (and the batteries are good) you should be seeing a series of numbers that correspond with the speed the platter is spinning. So assuming you've got your turntable set for 33.33 RPM you should see a "33" displayed that is stationary (indicating steady speed) or floats slowly left or right depending on whether your turntable is running fast or slow. Not sure what you mean by " the lines on the strobe bounce back and forth."
Tom