It varys by state, and states are allowed to set their own interpertations of the rules. For most states though, speed limits are in effect from the moment you pass the speed limit sign, and only apply to the direction of travel that sign applies to. Or at any rate where the sign is supposed to be. Also speed limit signs generally apply for the entire duration of the length of road until the next intersection. The theory being that if someone turns onto the road after the sign is posted, they wouldn't know the speed limit.
So, for example, in Washington, rural area speed limits are by law 50MPH unless posted otherwise, rural areas being defined as any rural road outside incorporated city limits. So if I exit the 70 MPH freeway onto a rural road and i do not see a speed limit sign, the limit is 50MPH. If I see a 35MPH sign ahead of me, I am legal to continue traveling 50MPH right up until my front bumper crosses the sign post plane. Physics of course make that somewhat difficult. Now the tricky part is that if the appropriate authorities placed a sign, and 3 minutes before I got there some drunk driver ran the sign over and it is no longer in place or visible, I am still required to obay the 35 MPH speed limit in theory. In actuallity, if no sign was visible you would have to probably go to court to contest the ticket, but most police officers wouldn't give youone, and most judges would rule in your favor due to the missing sign. Our 35 MPH speed limit is in force until we get to an intersection 3 miles ahead, where someone could turn onto the same stretch of road we travelling on. At that point, in most states, without a new posted speed limit sign, the speed limit would revert back to the generic rural area speed limit, in this case 50 MPH.
Speed limits do vary sometimes even on a 2 lane road. In a long curve, one of the lanes will be in a tighter radius than the other. This effect gets magnified if there is a large center median or turn lane, etc. It's unusual to find a major speed discrepancy though, so likely either someone hit the sign, stole the sign for metal content, or the lower sign on the one side was illegally put up by someone who thinks the speed limit is too high on that stretch of road.
if you run into an ambigous signing situation, call the county road maintenance office and ask. usually if nothing else that will get them out there with new speed limit signs to make things less confusing.
Other things to consider, you are required to obay the speed limit whether the sign is visible or not, but the appropriate government agency that maintains whatever stretch of road is also required to maintain signs in good working order and comply with minimum sight line distances (meaning that X speed sign must be visible for so many feet before you get to it, allowing you time to slow down, that usually varies based on the speed and the amount of change from the last posted limit). If there is a bush obsuring a speed limit sign and you ever get nabbed for speeding, thats usually an automatic get out of ticket free pass.
Edited, May 5th 2012 5:21pm by Kaolian