What relationship do frequency and wavelength have?

The relationship between frequency and wavelength is described by the wave equation, which states that the speed of a wave is equal to its frequency multiplied by its wavelength. This relationship can be mathematically expressed as ( v = f \lambda ), where ( v ) is the wave speed, ( f ) is the frequency, and ( \lambda ) is the wavelength.

When considering this equation, frequency and wavelength are inversely proportional. This means that if the frequency of a wave increases (indicating that more wave crests pass a given point per second), the wavelength must decrease to maintain the constant speed of the wave, assuming the wave medium does not change. Conversely, if the frequency decreases, the wavelength increases. Thus, as one quantity rises, the other must fall to keep the equation balanced.

This inverse relationship is a fundamental principle in wave mechanics, and it helps to understand phenomena such as how different colors of light can be related to their frequencies and wavelengths. Knowing this relationship allows us to predict how changes in one variable will affect the other, which is crucial for applications in physics and engineering.