Bumpiness in rear bicycle tire

my father and i recently refurbished a 1979 Schwinn Le Tour 12.2. I took it on a really long ride today and realized that the rear tire goes bump every time it goes around. I thought we had taken care of this problem by replacing the rear axel and adjusting the cups and cones correctly (before they had been so maladjusted that the bearings were cutting into the axel, therefore it had to be replaced). I've examined the bike and cannot find any visible problem: the wheel isnt rubbing against a stay, the tire is not flat, the chain is on ok, the rims arent rubbing against the brake pads...so im not sure what it is. I know that i need to replace my free wheel, could that possibly be the issue? Or maybe I just have a worn tube?

The wheel could still be out of round in the radial dimension rather than side to side. That can be fixed with spoke adjustment (a little tricky if you've never done it.....). It should be visible if you elevate the wheel and spin it.

Another thought, if you're feeling the bump in the pedals rather than your butt, you could have a sticky link in the chain that's causing a bump in the drivetrain. You may be able to fix that with lubrication, or it may require chain replacement

How big of a bump? It could be a wheel issue. I'll assume that the tires are new, but make sure you look at them. I rode my last set so long I wore straight through to the bead and the tire started to let go, creating a bulge and causing a bump every time it rotated.

Yeah! the previous answer seems correct. It could be stiff chain.

Check these videos:
http://bicycletutor.com/guide/

and this : http://bicycletutor.com/stiff-chain-link...

Perhaps the tire is not seated evenly in the rim. That would cause a flat spot and give you a bumpy ride. I am surprised there is no visible evidence when you have the bike off the ground and spinning the wheel with the pedals.
Tight link may be the cause, but that would be related to pedal speed, not wheel speed.
Just read your last sentence.
Remove the tubes from the tires and inflate. I have seen thin spots on an inner tube that blow up like a balloon. That will translate to a high spot on the tire.
Let us know what you find to be the problem.
MC

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