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

Answer 1

To find the wavelength of the radio waves, we can use the relationship between the speed of a wave, its frequency, and its wavelength, which is given by the formula:

\[
v = f \lambda
\]

Where:
- \( v \) is the speed of the wave,
- \( f \) is the frequency of the wave,
- \( \lambda \) is the wavelength of the wave.

We can rearrange this formula to solve for the wavelength \( \lambda \):

\[
\lambda = \frac{v}{f}
\]

Given:
- Frequency \( f = 9.23 \times 10^7 \) Hz
- Speed of the wave \( v = 3.00 \times 10^8 \) m/s

Now, substitute the values into the equation:

\[
\lambda = \frac{3.00 \times 10^8 \, \text{m/s}}{9.23 \times 10^7 \, \text{Hz}}
\]

Calculating this gives:

\[
\lambda = \frac{3.00 \times 10^8}{9.23 \times 10^7} \approx 3.25 \, \text{m}
\]

Therefore, the wavelength of the waves is:

\[
\lambda \approx 3.25 \, \text{m}
\]

The answer is **3.25 m**.