The relationship between the wavelength (λ) and the frequency (f) of a wave is defined by the wave equation:
v = λf
where:
- v represents the velocity or speed of the wave,
- λ represents the wavelength of the wave, and
- f represents the frequency of the wave.
This equation states that the velocity of a wave is equal to the product of its wavelength and frequency. The velocity of a wave is a constant value determined by the properties of the medium through which the wave is propagating. In a vacuum, electromagnetic waves (including light) travel at the speed of light, denoted by the symbol "c" and approximately equal to 3 x 10^8 meters per second.
From the wave equation, we can derive the relationship between wavelength and frequency as follows:
v = λf λ = v/f
This equation indicates that the wavelength of a wave is inversely proportional to its frequency. In other words, as the frequency of a wave increases, its wavelength decreases, and vice versa. This relationship holds true for all types of waves, including electromagnetic waves (such as light) and mechanical waves (such as sound waves).
For example, in the case of light, different colors correspond to different wavelengths. Red light has a longer wavelength and lower frequency, while blue light has a shorter wavelength and higher frequency. This relationship between wavelength and frequency is fundamental to understanding the nature of waves and their behavior.