Question

the diagram below shows the electromagnetic spectrum. based on this diagram, predict the relationship between the wavelength and frequency of a wave. explain your evidence and reasoning.

Explanation:

Step1: Observe the diagram

As we move from left - to - right on the electromagnetic spectrum diagram, the wavelength decreases (from radio waves with long wavelengths to gamma rays with short wavelengths). At the same time, the frequency increases (from low frequencies of radio waves to high frequencies of gamma rays).

Step2: Recall wave formula

The speed of a wave $v$ is related to its wavelength $\lambda$ and frequency $f$ by the formula $v = f\lambda$. In a given medium (for electromagnetic waves in a vacuum, $v = c\approx3\times 10^{8}\ m/s$ is constant). So, when $v$ is constant, if $\lambda$ decreases, $f$ must increase to keep the product $v = f\lambda$ constant.

Answer:

The relationship between the wavelength and frequency of a wave is an inverse relationship. As the wavelength of a wave increases, its frequency decreases, and vice - versa, because the speed of the wave (in a given medium) is constant and is given by the formula $v = f\lambda$.