Question

Radio waves travel at the speed of light, 3 x 108 meters/second. If your favorite radio station is
broadcast at a frequency of 101.5 megahertz (101.5 x 106 hertz), what is the wavelength of the radio
waves?
Answers below:
0.338 m

0.300 m

2.96 m

0.030 m

Answer 1

To calculate the wavelength of the radio waves, we can use the formula that relates the speed of light (c), frequency (f), and wavelength (λ):

\[
c = f \cdot \lambda
\]

Where:
- \( c \) is the speed of light (approximately \( 3 \times 10^8 \) meters per second),
- \( f \) is the frequency in hertz,
- \( \lambda \) is the wavelength in meters.

We can rearrange the formula to solve for wavelength:

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

Given the frequency of the radio station is \( 101.5 \) megahertz, we first convert that into hertz:

\[
f = 101.5 \times 10^6 \text{ Hz}
\]

Now, we substitute the values into the wavelength formula:

\[
\lambda = \frac{3 \times 10^8 \text{ m/s}}{101.5 \times 10^6 \text{ Hz}}
\]

Calculating this gives:

\[
\lambda \approx \frac{3 \times 10^8}{101.5 \times 10^6} \approx \frac{3 \times 10^8}{1.015 \times 10^8} \approx 2.95 \text{ m}
\]

After rounding, we find:

\[
\lambda \approx 2.96 \text{ m}
\]

Therefore, the correct answer is:

**2.96 m**