Why does wavelength decrease when frequency increases and relationship between the speed, frequency, and wavelength of a wave?
The wavelength is the distance the wave travels while the phase changes between the same values – the period of the wave. In a vacuum, the speed of the electromagnetic wave is 299792458 m/s, and the time of one period is 1/f. Therefore, wavelength λ=c/f and wavelength decreases when frequency increases. For a non-vacuum medium, the speed of the wave must be corrected with the permittivity of the medium ε: c/√ε.
The frequency is how many cycles the wave goes through in one second. They are inversely proportional meaning that the higher the frequency the lower the wavelength and vice versa. This is because if the wavelength is longer that means the wave goes through less cycle if the period of time (1 sec) remains the same. Because there is an inverse relationship between frequency and wavelength and frequency have the units of cycles per second. If you double the frequency there needs to be twice as many cycles per unit time. This is because the wave has to cover more distance in the same amount of time. Conversely, if the speed decreases while the frequency remains constant, the wavelength must decrease. This is because the wave covers less distance in the same amount of time. So, if the wavelength of a light wave is shorter, that means that the frequency will be higher because one cycle can pass in a shorter amount of time. This means that more cycles can pass by the set point in 1 second. Wavelength of a wave decreases when frequency increases and wavelength of a wave increases when frequency decreases. As the frequency increases, the distance between consecutive wave crests or troughs decreases. As the frequency decreases, the distance between consecutive wave crests or troughs increases. So, if the wavelength of a light wave is shorter, that means that the frequency will be higher because one cycle can pass in a shorter amount of time. This means that more cycles can pass by the set point in 1 second. The frequency and wavelength are indirectly proportional to each other. More is the wavelength, lesser is the frequency and vice-versa. The speed at which a wave travels is equal to the product of its frequency and wavelength, which justifies the link between these two parameters. Frequency is the characteristic of the source while wavelength is the characteristic of the medium. when monochromatic light travels from one medium to another its speed changes so its wavelength (λ=cv) changes but frequency v remains unchanged. Because the velocity is constant, any increase in frequency results in a subsequent decrease in wavelength. Therefore, wavelength and frequency are inversely proportional. The frequency of a wave is inversely proportional to its wavelength. That means that waves with a high frequency have a short wavelength, while waves with a low frequency have a longer wavelength. Frequency and wavelength are inversely proportional. The wave speed is equal to the product of its frequency and wavelength. All waves can be defined in terms of their frequency and intensity. c=λν expresses the relationship between wavelength and frequency. Wave speed is represented by the variable v, frequency (cycles per second) by f, and wavelength (cycle length) by the Greek letter λ. So v = f * λ or solving for λ, the equation becomes λ = v / f. Wave speed has units of distance per unit time, for example, meters per second or m/s.Wave speed is directly proportional to frequency and inversely proportional to wavelength. In more detail, the speed of a wave is determined by its frequency and wavelength.
I think that the distance that waves travel does not directly depend on frequency. Any wave will travel the same distance for the unit of time in the given medium. EM wave speed may depend slightly on the frequency due to medium permittivity dependence of frequency and even be variable during long travel distances, however, it is a special case and it is beyond current discussion. Frequency for this consideration is only a number of direction changes for electrical current. In a bit deeper look, it is half of the zero crossings for field intensity of waves electrical and magnetic components. For many cases of high-frequency signal analyses, zero crossing is an important factor.
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