How does frequency relate to wavelength in wave motion?

Frequency and wavelength are fundamentally related through the wave equation, which states that the speed of a wave (v) is the product of its frequency (f) and wavelength (λ). This relation can be expressed mathematically as:

[ v = f \cdot λ ]

From this equation, if the speed of the wave remains constant (which is true for waves traveling through the same medium), an increase in frequency corresponds to a decrease in wavelength and vice versa. This relationship demonstrates that frequency and wavelength are inversely related: as one increases, the other decreases to keep the wave speed constant.

This principle applies to all types of waves, from sound waves to electromagnetic waves. Understanding this inverse relationship is crucial in various fields, including physics, engineering, and telecommunications, as it helps explain phenomena such as pitch in sound and color in light.