A radio station, 98.1 on the FM dial, has radio waves with a frequency of 98.1 million cycles per second. Write an equation in the form [tex]d = \sin(\omega t)[/tex] for the simple harmonic motion of the radio waves.

To write an equation for the simple harmonic motion of radio waves with a frequency of 98.1 million cycles per second, we need to determine the angular frequency, [tex]$\omega$[/tex].

1. Identify the frequency:
- The frequency ([tex]$f$[/tex]) of the radio wave is given as 98.1 million cycles per second. In scientific notation, this is:
[tex]\[
f = 98.1 \times 10^6 \text{ cycles per second}
\][/tex]

2. Calculate the angular frequency ([tex]$\omega$[/tex]):
- The relationship between frequency and angular frequency is given by the formula:
[tex]\[
\omega = 2\pi f
\][/tex]
- Substituting the given frequency into the formula, we calculate:
[tex]\[
\omega = 2\pi \times 98.1 \times 10^6
\][/tex]

3. Result of the angular frequency:
- The computed angular frequency ([tex]$\omega$[/tex]) is approximately:
[tex]\[
\omega \approx 616,380,478.63
\][/tex]

4. Write the equation of simple harmonic motion:
- The equation for simple harmonic motion is given by:
[tex]\[
d = \sin(\omega t)
\][/tex]
- Using the calculated angular frequency, the equation becomes:
[tex]\[
d = \sin(616,380,478.63 \times t)
\][/tex]

This equation represents the simple harmonic motion of the radio waves with the given frequency.