The relationship between frequency and wavelength in a wave is inversely proportional, encapsulated by the equation \( v = f \lambda \), where \( v \) is the wave's speed, \( f \) is its frequency, and \( \lambda \) is its wavelength. As frequency increases, wavelength decreases and vice versa. This relationship is fundamental in understanding various types of waves, including sound and electromagnetic waves. The speed of the wave remains constant in a given medium, which allows us to predict how changes in frequency will affect wavelength, influencing phenomena such as color perception in light waves or pitch in sound waves.