The product of frequency and wavelength being equal to the velocity of light is a fundamental relationship that arises from the nature of electromagnetic waves. This relationship is known as the wave equation.
The wave equation states that the velocity (v) of a wave is equal to the product of its frequency (f) and wavelength (λ). Mathematically, it can be expressed as:
v = f * λ
For electromagnetic waves, including light, the wave equation holds true. The velocity of light in a vacuum is a constant denoted by "c," which is approximately 299,792,458 meters per second (m/s). Therefore, the equation can be written specifically for light as:
c = f * λ
This equation tells us that the speed of light remains constant regardless of changes in its frequency or wavelength. If the frequency increases, the wavelength must decrease to maintain the constant speed of light. Conversely, if the frequency decreases, the wavelength must increase.
This relationship is a consequence of Maxwell's equations, which describe the behavior of electromagnetic waves and their interaction with matter. Maxwell's equations, combined with experimental observations, led to the understanding that the speed of light in a vacuum is a fundamental constant of nature.