The product of frequency and wavelength being equal to the velocity of light is a fundamental property of electromagnetic waves. It arises from the relationship between the speed, frequency, and wavelength of a wave.
In the case of electromagnetic waves, such as light, the velocity of propagation is a constant value denoted by "c" and represents the speed of light in a vacuum. In SI units, the speed of light is approximately 299,792,458 meters per second.
The frequency of a wave refers to the number of complete oscillations or cycles that occur in a given unit of time. It is measured in hertz (Hz), where 1 Hz represents one cycle per second. The wavelength, on the other hand, is the distance between two consecutive points in the wave that are in phase, such as two crests or two troughs. It is usually denoted by the Greek letter lambda (λ) and is measured in meters.
The relationship between the velocity, frequency, and wavelength of a wave is given by the equation:
velocity = frequency × wavelength
For electromagnetic waves, including light, this equation can be expressed as:
c = f × λ
where "c" is the speed of light, "f" is the frequency of the wave, and "λ" is the wavelength of the wave.
Since the speed of light is constant, if you increase the frequency of light, the corresponding wavelength will decrease, and vice versa. This relationship allows for the conservation of energy and information carried by the wave. In other words, as the frequency increases, the energy per unit time carried by the wave remains constant, but the wave oscillates more rapidly, resulting in a shorter wavelength.
Thus, the product of frequency and wavelength is equal to the speed of light because that relationship is a fundamental property of electromagnetic waves.