An increase in frequency is directly related to a decrease in wavelength, and vice versa. This relationship is governed by the wave equation, which states that the speed of a wave is equal to the product of its frequency and wavelength. Mathematically, it can be expressed as:
Velocity (v) = Frequency (f) × Wavelength (λ)
Given this equation, if the frequency of a wave increases while the velocity remains constant, the wavelength must decrease to maintain the equality. Similarly, if the frequency decreases, the wavelength must increase.
Let's consider an example with sound waves. Sound travels at a constant speed in a given medium (such as air), so if the frequency of a sound wave increases, its wavelength will decrease. This means that the distance between successive crests or troughs of the wave becomes smaller. Conversely, if the frequency decreases, the wavelength becomes longer.
The same principle applies to other types of waves, such as electromagnetic waves (including visible light). If the frequency of an electromagnetic wave increases, the wavelength decreases, resulting in a shift towards higher-energy, shorter-wavelength waves (e.g., from red to blue light in the visible spectrum). On the other hand, if the frequency decreases, the wavelength becomes longer, leading to lower-energy, longer-wavelength waves.
In summary, an increase in frequency is accompanied by a decrease in wavelength, while a decrease in frequency corresponds to an increase in wavelength.