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The car will produce falttirelike noise without any tire issues for several reasons. One of the most common yet frequent reasons is older tires with less grip. In addition, there may have misaligned wheels, tire crossing over solid objects, starts separating the side wall, etc.

Why The Car Sounds Like It Has A Flat Tire But Doesn’t: Check Solutions
Loosen Objects Around The Trunk Or Hatch Area
Inappropriate Wheels Position
Sudden Braking
Faulty Tire Assembly
Loosen Serpentine Belt
Damaged Wheel Bearings And Ball Joints