Question

If the frequency of a radio station is 88.1 MHz (8.81 × 107 Hz), what is the wavelength of the wave used by this radio station for its broadcast? The answer should have three significant figures.

Answer 1

To find the wavelength of a radio wave, you can use the relationship between the speed of the wave, its frequency, and its wavelength. The formula is given by:

\[
\text{speed} = \text{frequency} \times \text{wavelength}
\]

For radio waves, the speed is typically the speed of light in a vacuum, which is approximately \( c = 3.00 \times 10^8 \, \text{m/s} \).

Given the frequency \( f = 88.1 \, \text{MHz} = 8.81 \times 10^7 \, \text{Hz} \), we can rearrange the formula to solve for wavelength \( \lambda \):

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

Substituting the values:

\[
\lambda = \frac{3.00 \times 10^8 \, \text{m/s}}{8.81 \times 10^7 \, \text{Hz}}
\]

Now, performing the calculation:

\[
\lambda \approx \frac{3.00}{8.81} \times 10^{8 - 7}
\]
\[
\lambda \approx 0.340 \times 10^{1}
\]
\[
\lambda \approx 3.40 \, \text{m}
\]

Thus, the wavelength of the wave used by this radio station is:

\[
\boxed{3.40 \, \text{m}}
\]