assuming all light travels at the same speed, would light with longer or shorter wavelengths have a higher…

Explanation:

Step1: Recall the wave - speed formula

The speed of a wave is given by $v = \lambda f$, where $v$ is the speed of the wave, $\lambda$ is the wavelength, and $f$ is the frequency.

Step2: Rearrange the formula for frequency

We can rewrite the formula as $f=\frac{v}{\lambda}$. Since the speed of light $v$ is constant (as given in the problem), frequency $f$ and wavelength $\lambda$ are inversely proportional.

Step3: Analyze the relationship

When $\lambda$ is smaller (shorter wavelength), the value of $\frac{v}{\lambda}$ (frequency $f$) is larger. When $\lambda$ is larger (longer wavelength), the value of $\frac{v}{\lambda}$ (frequency $f$) is smaller.

Answer:

Light with shorter wavelengths has a higher frequency because the speed of light is constant and frequency and wavelength are inversely - proportional according to the formula $f = \frac{v}{\lambda}$.