Question

an fm radio station broadcasts at 9.23 × 10⁷ hz. given that the radio waves travel at 3.00 × 10⁸ m/s, what is the wavelength of these waves?
0.308 m
2.77 m
3.25 m
6.50 m

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 rewrite the formula as \(\lambda=\frac{v}{f}\).

Step2: Substitute the given values

We are given that \(v = 3.00\times10^{8}\ m/s\) and \(f=9.23\times 10^{7}\ Hz\).
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: Calculate the wavelength

Using the rules of exponents \(\frac{a^{m}}{a^{n}}=a^{m - n}\), we have \(\frac{3.00\times 10^{8}}{9.23\times 10^{7}}=\frac{3.00}{9.23}\times10^{8 - 7}\).
\(\frac{3.00}{9.23}\approx0.325\) and \(10^{8 - 7}=10^{1}\).
So \(\lambda\approx0.325\times10^{1}=3.25\ m\).

Answer:

C. \(3.25\ m\)