The relationship between wavelength and frequency in electromagnetic radiation is determined by the nature of the wave and the medium through which it propagates. In the case of electromagnetic waves, including light, the wavelength decreases as the frequency increases. This relationship is described by the equation:
c = λν
where c is the speed of light, λ (lambda) is the wavelength, and ν (nu) is the frequency.
The reason for this inverse relationship is rooted in the fundamental properties of electromagnetic waves. Electromagnetic waves consist of oscillating electric and magnetic fields that are perpendicular to each other and to the direction of wave propagation. These fields interact with each other and propagate through a vacuum or a medium at the speed of light.
As the frequency of the electromagnetic wave increases, it means that more oscillations occur in a given time period. Consequently, the distance between consecutive peaks or troughs (wavelength) becomes shorter, leading to a decrease in wavelength as frequency increases.
On the other hand, for sound waves and longitudinal vibrations, the situation is different. Sound waves are mechanical waves that require a medium, such as air, water, or solids, for their propagation. In a medium, sound waves are created by the compression and rarefaction of the particles of the medium, resulting in longitudinal vibrations.
The speed of sound in a medium depends on the properties of that medium, such as its density and elasticity. The wavelength of a sound wave is related to the speed of sound and the frequency by the equation:
v = λf
where v is the speed of sound, λ (lambda) is the wavelength, and f is the frequency.
In the case of sound waves, the speed of sound in a given medium remains relatively constant for a given set of conditions. Therefore, as the frequency increases, the wavelength must increase to maintain the relationship between the speed of sound, wavelength, and frequency. This means that in sound waves, higher frequencies correspond to longer wavelengths.
In summary, the inverse relationship between wavelength and frequency in electromagnetic waves is a consequence of the nature of electromagnetic waves and their propagation through vacuum or a medium at the speed of light. In contrast, for sound waves and longitudinal vibrations, the speed of sound in a medium determines the relationship between wavelength and frequency, leading to longer wavelengths for higher frequencies.