1989 Yes it’s an old car and makes a wop wop wop sound as it starts and slows. Vibration can be felt through the floor, more so on passenger side. Sound and vibration go away when car reaches 15 or 20 mph, then returns on slowing.
I’d start by closely inspecting the tires. A defect in a tire can make a noise such as you describe.
Why do you think it’s the transmission?
I agree with mc. It also could be a brake issue.
I agree that this is most likely to be a brake issue or a tire problem.
However, if you live in fear of transmission problems, I want to add that you should be changing the transmission fluid and filter every 25-30k in order to extend the life of that trans.
If you are not doing this, you are simply inviting transmission failure anytime after the odometer hits 90k, and replacing the transmission on this car might mean that you have to take a second mortgage on your house.
Maintenance is far cheaper than repairs, and peace-of-mind is very much preferable to anxiety.