Wavelength (λ), frequency (f), speed (v), and wave number (k) are interconnected properties of a wave and are related through the following formulas:
Wavelength and Frequency: The wavelength of a wave is inversely proportional to its frequency. The relationship is given by the equation: λ = v / f where λ represents the wavelength, v represents the speed of the wave, and f represents the frequency. This equation states that as the frequency of a wave increases, its wavelength decreases, and vice versa, provided the speed remains constant.
Speed and Frequency: The speed of a wave is directly proportional to its frequency. The relationship is expressed by the equation: v = λ * f where v represents the speed, λ represents the wavelength, and f represents the frequency. This equation indicates that as the frequency of a wave increases, its speed also increases, provided the wavelength remains constant.
Wave Number: The wave number (k) is a measure of the spatial frequency of a wave. It is defined as the reciprocal of the wavelength, represented by the equation: k = 2π / λ where k represents the wave number, and λ represents the wavelength. The wave number is commonly used in wave equations and Fourier analysis to describe wave phenomena mathematically.
In summary, wavelength and frequency are inversely related, while speed and frequency are directly related. The wave number is defined as the reciprocal of the wavelength. These relationships allow us to describe and analyze wave behavior in different mediums.