A wave is a disturbance that propagates from its source, repeating itself periodically, and is typically associated with simple harmonic motion. Mechanical waves are governed by Newton's laws and require a medium to travel. A medium is a substance in which a mechanical wave propagates, and the medium produces an elastic restoring force when it is deformed.
Water waves, sound waves, and seismic waves are some examples of mechanical waves. For water waves, the wave propagation medium is water; for sound waves, the medium is usually air, but could also be water. The wave disturbance in sound waves is generally a change in air pressure. In the case of mechanical waves, both energy and momentum are transferred with the wave's motion, whereas the mass oscillates around an equilibrium point.
Waves can be transverse, longitudinal, or a combination of the two. For example, the waves on the strings of musical instruments are transverse. Meanwhile, sound waves in air and water are longitudinal; their disturbances are periodic variations in pressure that are transmitted in fluids. Fluids do not have appreciable shear strength, and thus, the sound waves in them must be longitudinal or compressional. However, sound waves that travel in solids can be both longitudinal and transverse.
Earthquake waves under the Earth's surface also have both longitudinal and transverse components. These components have important individual characteristics—they propagate at different speeds. Earthquakes also have surface waves that are similar to surface waves on water.
This text is adapted from Openstax, University Physics Volume 1, Section 16.1: Traveling Waves.
