This is a classic bad wheel bearing sound. Turning left or right should make the whomp whomp stop or become less noticeable when the bad bearing is unloaded. In other words turning right will load up the left wheel as the car keels over to the left, and vicversa.
As suggested previously, remove suspected races and bearings from hub and drum, clean them than look for discoloration, pitting, grinding or rough feel when bearing is turned by hand, all signs that the bearing is no good, and needs to be replaced.
Vibration could be caused by not properly tightening wheel bearing which will destroy the bearing after a while.