spherical , cylindrical wave

Plane, spherical and cylindrical are description of the geometrical shape of the wavefronts.

This, a plane wave with wavefronts in the form of flat planes. A spherical wave has wavelengths in the form of a series of spheres moving outward from a common centre. Cylindrical wave has wavefronts in the forms of a series of cylinders moving outward from a common axis.

Examples:
Plane wave: water waves in a ripple tank produced by a vibrating flap.
Spherical wave: light wave from a light bulb.
Cylindrical wave: sound waves after diffraction at an rectangular opening.

The intensity of spherical wave follows the "inverse square law", i.e. intensity is inversely proportional to square of distance from the wave source. Since amplitude of wave is proportional to the square root of intensity, it follows that amplitude is inversely proportional to the distance from the source.

For cylindrical waves, intensity is inversely proportional to the distance from the source. Hence, wave amplitude is inversely proportional to the square root of the distance from the source.