an fm radio station broadcasts at 9.23×10⁷ hz. given that the radio waves travel at 3.00×10⁸ m/s, what is…

Explanation:

Step1: Recall wave - speed formula

The wave - speed formula is $v = f\lambda$, where $v$ is the speed of the wave, $f$ is the frequency, and $\lambda$ is the wavelength. We need to solve for $\lambda$, so $\lambda=\frac{v}{f}$.

Step2: Substitute given values

We are given that $v = 3.00\times10^{8}\text{ m/s}$ and $f = 9.23\times10^{7}\text{ Hz}$. Substituting these values into the formula $\lambda=\frac{v}{f}$, we get $\lambda=\frac{3.00\times 10^{8}}{9.23\times 10^{7}}$.

Step3: Perform the calculation

Using the rules of exponents for division ($\frac{a\times10^{m}}{b\times10^{n}}=\frac{a}{b}\times10^{m - n}$), we have $\frac{3.00}{9.23}\times10^{8 - 7}\approx0.325\times10^{1}=3.25\text{ m}$.

Answer:

C. 3.25 m