The speed of a wave is directly proportional to both its frequency and its wavelength.

The speed at which a wave propagates is determined by the medium through which it travels. In a vacuum, electromagnetic waves travel at the speed of light, which is approximately $3 \times 10^8 \, \text{m/s}$. In other media, such as air or water, the speed of a wave is slower and varies depending on the properties of the specific medium.

The frequency of a wave refers to the number of complete cycles it undergoes in one second and is measured in Hertz (Hz). Conversely, the wavelength of a wave is defined as the distance between two consecutive points on the wave that are in phase, such as two adjacent crests or two consecutive troughs. Wavelength is measured in meters (m).

The relationship among the speed of a wave, its frequency, and its wavelength is encapsulated by the equation:

where $v$ represents the speed of the wave, $f$ is the frequency, and $\lambda$ is the wavelength. This equation illustrates that as the frequency of a wave increases, its wavelength decreases, and vice versa. Importantly, the speed of the wave remains constant for a given medium.

Understanding this relationship is crucial for analyzing the behavior of waves and their interactions with different media. For instance, when a wave transitions from one medium to another, its speed may change, but its frequency and wavelength will remain unchanged. This phenomenon can lead to refraction or reflection of the wave, resulting in observable effects such as the bending of light or the echoes produced by sound waves.