The simplest mechanical waves are associated with simple harmonic motion and repeat themselves for several cycles. These simple harmonic waves can be modeled using a combination of sine and cosine functions. Consider a simplified surface water wave that moves across the water's surface. Unlike complex ocean waves, in surface water waves, water moves vertically, oscillating up and down, whereas the disturbance of the wave moves horizontally through the medium. If a seagull is floating on the water, the waves cause the seagull to move up and down in simple harmonic motion as the wave’s crests and troughs (peaks and valleys) pass under the bird.

There are several different parameters associated with waves. The time for one complete oscillation of the up-and-down motion is called the wave period. In addition, wave frequency is the number of waves that pass through a point per unit of time. The wave period is usually measured in seconds, although can be expressed using any convenient unit of time, while frequency is usually measured in hertz (Hz). The length of a wave is called the wavelength, which is measured in any convenient unit of length, such ascentimeters or meters. The amplitude of a wave is a measure of the maximum displacement of the medium from its equilibrium position. Like wavelength, the amplitude can be measured in centimeters, meters, or any other convenient unit of distance.

This text is adapted from Openstax, University Physics Volume 1, Section 16.1: Traveling Waves.