Question

1 formula 1 point
mr. phsters favorite radio station is 97 mhz. what is the wavelength of mr. phsters favorite radio station? use the wave equation from the notes as well as the speed of light = 3×10⁸ m/s. (do not put any units with your answer.)
answer

Explanation:

Step1: Recall the wave equation

The wave equation is \( c = \lambda
u \), where \( c \) is the speed of light, \( \lambda \) is the wavelength, and \(
u \) is the frequency. We need to solve for \( \lambda \), so we rearrange the formula to \( \lambda=\frac{c}{
u} \).

Step2: Convert frequency to SI units

The frequency \(
u = 97\space MHz \). Since \( 1\space MHz = 10^{6}\space Hz \), we convert \( 97\space MHz \) to \( Hz \): \(
u = 97\times10^{6}\space Hz \).

Step3: Substitute values into the formula

We know that \( c = 3\times10^{8}\space m/s \) and \(
u = 97\times10^{6}\space Hz \). Substituting these values into \( \lambda=\frac{c}{
u} \), we get:
\[
\lambda=\frac{3\times10^{8}}{97\times10^{6}}
\]
Simplify the expression:
\[
\lambda=\frac{3\times10^{2}}{97}=\frac{300}{97}\approx 3.09
\]

Answer:

\( 3.09 \) (or a more precise value like \( \frac{300}{97}\approx3.0928 \) depending on rounding, but \( 3.09 \) is a reasonable approximation)