2000 Mercury Grand Marquis - Wash board

Wash board affect from 30 to 65 mph. what could be causing this?

I have no idea what washboard effect means to you. Please explain more fully and also tell us some details about the car and service it had.

My money is on a tire in need of balancing or replacement.

Perhaps, or perhaps the OP is trying to describe the effect of a failed torque converter lockup mechanism. Without more details from the OP, we are all just taking guesses in the dark, so to speak.

Sometimes bad wheel bearing can cause that. Its like if you are driving on a rumble strip on the edge of the highway.My Astro van did exactly that with a bad wheel bearing.

The problem might be with a worn out shock absorber causing tire bounce.

Tester

Tires different sizes or brands? I replaced two tires on an 1986 Dodge Colt (155/80R13). The tires were the correct size but a different brand than the other two tires. Driving home the car would start shaking at 40-45 mph.

Once I replaced the other two tires so all four were the same the shaking stopped.

Ed B.