5. complete each statement for an electromagnetic wave in space: a. if the wavelength increases, frequency…

Explanation:

Step1: Recall wave - speed formula

The speed of an electromagnetic wave in space is given by $v = f\lambda$, where $v$ is the speed, $f$ is the frequency and $\lambda$ is the wavelength. In space, the speed of electromagnetic waves is the speed of light $c$, so $c = f\lambda$.

Step2: Analyze part a

From $c = f\lambda$, we can express $f=\frac{c}{\lambda}$. Since $c$ is constant in space, when $\lambda$ increases, $f$ decreases.

Step3: Analyze part b

From $c = f\lambda$, we can express $\lambda=\frac{c}{f}$. Since $c$ is constant in space, when $f$ increases, $\lambda$ decreases.

Step4: Analyze part c and d

The speed of an electromagnetic wave in space is a constant, the speed of light $c\approx3\times 10^{8}\ m/s$. So, whether the wavelength increases or decreases, the speed stays the same.

Answer:

a. decreases b. decreases c. stays the same d. stays the same