A pneumatic tire and a rim includes a noise damper, fixed to a tire inner surface or a rim inner surface with the upper surface facing a tire inner space, and extending in the tire circumferential direction. The noise damper is made of a sponge having a volume ranging from 0.4 to 20% of the volume of the tire inner space. The noise damper is a laterally long and flat, with a maximum thickness ranging from 5 to 45 mm and a width more than the maximum thickness. The upper surface extends along a wavy curve including a hilltop, valley bottoms on each side of the hilltop and slopes extending down to the respective valley bottoms from the hilltop. Each end of the upper surface is terminated at the valley bottoms or the slopes. A thickness from the upper surface to the bottom surface ranges from 1.0 to 15.0 mm.