Which variable is used to describe how fast a wave travels through a medium?

The variable that describes how fast a wave travels through a medium is speed. In the context of wave physics, speed refers to the rate at which the energy or information carried by the wave propagates through a given medium. It is defined as the distance traveled by the wave per unit of time.

In wave mechanics, the relationships between speed, wavelength, and frequency are critical. The speed of a wave can be expressed mathematically as the product of its wavelength and frequency. This relationship highlights that while wavelength and frequency are crucial properties of wave behavior, speed specifically addresses the velocity at which the wave moves through a medium.

The other options—period, wavelength, and intensity—represent different characteristics of waves. Period refers to the time it takes for one complete cycle of the wave to pass a given point, wavelength is the distance between successive crests or troughs of the wave, and intensity measures the power per unit area carried by the wave. While all these terms are related to the description of waves, they do not specifically denote how fast the wave travels through a medium, making speed the correct choice for this question.