an fm radio station broadcasts at 9.23×10^7 hz. given that the radio waves travel at 3.00×10^8 m/s, what is…

Explanation:

Step1: Recall the 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 we can re - arrange the formula to $\lambda=\frac{v}{f}$.

Step2: Identify the values of $v$ and $f$

We are given that $v = 3.00\times10^{8}\ m/s$ and $f = 9.23\times10^{7}\ Hz$.

Step3: Substitute the values into the formula

$\lambda=\frac{3.00\times 10^{8}\ m/s}{9.23\times 10^{7}\ Hz}$ First, divide the coefficients: $\frac{3.00}{9.23}\approx0.325$. Then, divide the powers of 10 using the rule $\frac{10^{a}}{10^{b}}=10^{a - b}$, so $\frac{10^{8}}{10^{7}}=10^{8 - 7}=10^{1}$. $\lambda\approx0.325\times10^{1}\ m = 3.25\ m$

Answer:

3.25 m