Wave motion is doubly periodic. Explain

Hint The transfer of momentum and energy of a medium from one point to the other without the transfer of matter is called wave motion. Based on the media of propagation, the dimension of propagation of wave energy, and the transfer of energy wave motion can be classified into three.

Complete step by step answer:
The time taken for the execution of one complete cycle is called the period of the wave. The wave motion will be repeated after a particular interval of time. Hence we can say that wave motion is periodic in time.
If we consider the same state of motion, the distance between two consecutive points will be the same. Their phase will always be the same. The constant distance between the two points can be called the wavelength of the wave. The interval of distance will also be the same in a wave motion. That means the distance is also periodic. Hence we can say that the wave motion is periodic in space also.
The wave motion is periodic in both time and in space that’s why we call wave motion doubly periodic.

Additional Information
The wave velocity is not the same as particle velocity. In a given medium the velocity of the wave will be a constant. The velocity of the particle will not be the same, it will be maximum in the mean position and it will be minimum in the extreme positions.

Note
When a wave is traveling between two media, as it transfers from one media to the other the wavelength and the speed of the wave will change. But the frequency of the wave will not change due to this transfer between media. The frequency will depend on the source of the wave.