The product of frequency and wavelength is equal to the velocity of light because of the fundamental relationship between these quantities in the context of electromagnetic waves. This relationship is described by the equation:
velocity = frequency × wavelength
This equation, known as the wave equation, applies to any type of wave, including electromagnetic waves such as light. In the case of light, the velocity refers to the speed at which light travels, commonly denoted as the speed of light (c).
Frequency (f) refers to the number of complete cycles of the wave that occur in one second. It is measured in units of hertz (Hz). Wavelength (λ), on the other hand, is the distance between two corresponding points on the wave, such as the distance between two peaks or two troughs. It is typically measured in units of meters (m).
When you multiply the frequency of light by its wavelength, you obtain a value that corresponds to the speed of light, which is approximately 299,792,458 meters per second (m/s). This relationship holds true for all electromagnetic waves, as they all travel at the same speed in a vacuum, known as the speed of light.
Mathematically, the equation can be expressed as:
c = f × λ
Where: c = velocity of light (speed of light) f = frequency of the electromagnetic wave λ = wavelength of the electromagnetic wave