Describe the relationship between wavelength and frequency.

Wavelength and frequency have an inverse relationship; as the frequency of a wave increases, its wavelength decreases.

In the realm of physics, particularly in the study of waves, the relationship between wavelength and frequency is a fundamental concept. Wavelength, denoted by the Greek letter lambda (λ), is the distance between two successive points in a wave that are in the same phase. This could be the distance between two crests or two troughs. Frequency, on the other hand, represented by the symbol 'f', is the number of waves that pass a given point per unit of time, typically per second (also known as Hertz, Hz).

The relationship between these two quantities is governed by the wave equation, v = fλ, where 'v' is the speed of the wave. This equation tells us that the speed of a wave is equal to the product of its frequency and wavelength. Therefore, if the speed of the wave is constant, as is the case with light in a vacuum, an increase in frequency will result in a decrease in wavelength, and vice versa. This is known as an inverse relationship.

To visualise this, imagine a wave on a string. If you start to shake the end of the string faster (increasing the frequency), the waves will become closer together, decreasing the wavelength. Conversely, if you shake the string slower, the waves will spread out, increasing the wavelength. This is a simple demonstration of the inverse relationship between frequency and wavelength.

In the context of light waves, this relationship explains the different colours we see. Light with a high frequency (and therefore short wavelength) appears blue or violet, while light with a low frequency (and long wavelength) appears red. This is why we see a rainbow of colours in the visible light spectrum, from red at one end (long wavelength, low frequency) to violet at the other (short wavelength, high frequency).

Understanding the relationship between wavelength and frequency is crucial in many areas of physics, including quantum mechanics and electromagnetic theory. It allows us to understand and predict the behaviour of waves, from light and sound to radio and microwaves.