There are many physical phenomena that can be modelled by sine waves:

Waves in water are an obvious example,

Compression and rarefaction in the propagation of sound,

Transmission of all electromagnetic radiation,

Vibrations of strings in Musical Instruments,

Bodies "bouncing" on a spring.

Also, more complicated motion can be modelled by a superposition of many sine waves (using Fourier transforms). This enables complex motions to be studied more easily.