Question

An FM radio station broadcasts radio waves with a frequency of 96,000,000 Hz. What is the speed of these radio waves if they have a wavelength of 3.1 m?

Answer 1

To find the speed of the radio waves, we can use the wave equation:

\[
v = f \times \lambda
\]

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

Given:
- Frequency \( f = 96,000,000 \) Hz (or 96 MHz)
- Wavelength \( \lambda = 3.1 \) m

We can plug in the values:

\[
v = 96,000,000 \, \text{Hz} \times 3.1 \, \text{m}
\]

Now, performing the multiplication:

\[
v = 297,600,000 \, \text{m/s}
\]

So, the speed of the radio waves is \( 297,600,000 \) m/s.

In summary, the speed of the radio waves is approximately \( 2.976 \times 10^8 \) m/s or \( 297,600,000 \) m/s.