I have a knocking sound from my left rear wheel as I am driving up a pretty steep hill. This happened after I changed my tire. If I stop a couple of times, the noise slowly dies out and it doesn't make anymore noise, even if I traverse up a steep hill. It only happens when I drive it the next day. What's wrong?

they are not better, in vast usages, not told by you at all.(DOING WHAT?)
on ice.?
I have this Pickup with rear axle, lockers.(Eaton) and 4wd jeeps.
Many a time: (ME)
I am on steep hill, going down hill. on solid full ice at 31F and slippy as all heck, in fact, not worst it can be period! the HILL of H3LL.
I'm off the brakes. (can be horror on ice this , ABS can help)

and I am using 2nd gear(manual transmission rule) about 15mph and
using engine compression to slow me down,just like the feathers on an ARROW it and me going straight. rear lockers, both rear tires pulling to the rear.
just like the tail of a Kite, ever make one and fly one?

truck is stable and fully straight. on this steep hill of ice


and behold some kids in a HONDA car with FWD and now going down the hill backwards front tires, doing that nasty act. (car wants to spin and did)


FWD is to make cheaper cars,that is the reason, only. and faster assembly too.

AWD is best always. costs more but saves many lives every day.
FWD can be a great horror on ICE.

FWD steering action, can get into a war with the FWD axles. !
ever seen that happen in a bad moment. not fun ever when seen.

yes going up hill FWD can be a joy . but some times we go down hill even on ICE.
amazing no?

AWD wins,
or 4wd with lockers. center diff locked. (or Part time 4wd)_
or just rear locker, (for sure my chevy Eaton lockers)
my EATOn locker
even works on moss covered steep boat launch ramp with my crazy big heavy 22ft boat. both tires spin not just 1 ,see? pulling all that out of the bay.
even/Steven. clean and safe.

what matters most. is
what you do with a car or truck. and where, and driving what surfaces.
only that. and not told

RWD with lockers are great.
RWD with open axles stink on any kind of ice or snow or dirt.

they look the same (1st glance)but are NOT.

AWD is best for most persons. costs more but is MORE!

is gear shift if PARK?????
are front tires crushed to the curb??? we can not see that
key is not able to turn to ON, sure.
so to do that , we have to man handle the wheel.
(for sure at any curb)
hard left and hard right even 20 lbs of force. and at the same time gently wiggle the key to ON.
it will go if front tires, not down steep hill, pointing to a curb.
we can not see where you car is, so answers can get complex.
ever drive in San Francisco, I did in 1968 , thanks to MIL draft thing..
down hill parking there takes SKILLS,.
even getting out of PARK is even more hard there. that is a 2nd lock.

Assuming yours is the 2 gear stick layout this is roughly how it works.
ONLY CHANGE BETWEEN 2 AND 4 WHEEL DRIVE WHEN STOPPED, IN NEUTRAL AND WITH THE PARKING BRAKE ON!!
The smaller gear shift should be to the left of the normal gearstick.
It should be in the fully forward position. This means it is in 2 wheel drive, high ratio, for normal road driving. (Rear wheels).
Pulling the stick back ONE notch engages 4 wheel drive, high ratio. Used for snowy, icy, slippery conditions as well as light off roading. (Keep the speed under 50mph).
Pushing down and back another notch engages neutral in the transfer box. This means ALL drive is DISCONNECTED even if you use the normal gearbox.
**Try to avoid this one**!!
Pulling the stick back the last notch engages 4 wheel drive, LOW ratio. This is for the more extreme off roading conditions such as VERY steep hills. Not usually used in normal day to day driving.
The two fully forward positions, (2High and 4High), will be the ones used the most.

sound like you may have put different size tires/wheels on the rear than what is already on the front. It is critical that the front and rear wheels are the same size.

sounds like a bent axle

TAKE VECHICLE TO WHEEL ALIGNMENT CENTER.SOUND LIKE VECHICLE OUT OF LINE.COULD HAVE BAD WORN REAR WHEEL BEARING.

never get your money back out later if you dont do much offroad reduce rubber size smaller tire size.

I HAVE THE SAME PROBLEM I'VE BEEN DOING A LOT OF RESEARCH ON IT AND I THINK ITS GONNA BE THE BUSHINGS IN THE REAR KNUCKLE ASSEMBLY AND YOUR HAVE TO CHANGE THE WHOLE ASSEMBLY. I HAVEN'T TRIED IT YET BUT IF YOU CHECK BACK IN A COUPLE DAYS I WILL LET YOU KNOW

Hello Timothy...

Drop into your local tire shop and have the suspect tire and rim checked out. You may have knocked a balancing weight off or bent the rim.

Better safe than sorry.

Providing that the c/v joints are in good condition, the dealers diagnosis sounds reasonable. However, changing two tires may not solve the problem. In reality the rolling circumference of all four tires must match. Mating two new tires to two partially worn tires may get you closer but still not where you should be.
In four wheel drive vehicles, this situation becomes more critical because the transfer case cannot operate properly when front tires are going at a different speed than the rear ones. This can cause the t case to fail (far worse than your problem) Owners of 4x4's generally change all four tires even getting down to matching production lot #s when possible to ensure exact diameter match up. Tire sizes also vary from manufacturer to manufacturer same #s are not always the same size! Therefore using two tires of a different brand can cause a problem as well.
I haven't "cured" anything, but I hope this gives you a better understanding of what you are dealing with.
good luck.