What is the relationship between frequency and wavelength in waves?

The relationship between frequency and wavelength in waves is governed by the wave equation, which is often stated as ( v = f \lambda ), where ( v ) is the wave speed, ( f ) is the frequency, and ( \lambda ) is the wavelength. This equation illustrates that, for a given wave speed, frequency and wavelength are inversely related.

As the wavelength increases, the frequency must decrease to maintain a constant wave speed, which is typical for all waves traveling through a medium at a particular speed. Thus, if you stretch the wavelength of a wave (making it longer), you will have fewer wave cycles passing a point in a given time, leading to a decrease in frequency. This inverse relationship is fundamental to understanding wave mechanics.

In simple terms, when the wavelength increases (the distance between successive wave peaks becomes greater), the number of wave cycles per second (frequency) diminishes. This principle is essential when studying waves across various contexts, such as sound, light, and water waves.