What is the relationship between frequency and wavelength in waves?

The relationship between frequency and wavelength in waves is described by the equation ( v = f \lambda ), where ( v ) represents the wave speed, ( f ) is the frequency, and ( \lambda ) (lambda) is the wavelength. From this relationship, it becomes clear that frequency and wavelength are inversely related.

When the frequency of a wave increases, it means that more wave cycles pass a given point in a unit of time. As this happens, for the speed of the wave to remain constant, the wavelength must decrease; that is, the distance between successive wave crests becomes smaller. Conversely, if the wavelength increases, this implies that fewer wave cycles are passing by that point in the same time frame, indicating a decrease in frequency.

This inverse relationship highlights that as one parameter increases, the other must decrease in a consistent manner. This fundamental principle applies to all types of waves, including sound waves, light waves, and water waves, emphasizing the interconnectedness of frequency and wavelength within the broader context of wave behavior.