Question

amateur radio operators in the united states can transmit on several bands. one of those bands consists of radio waves with a wavelength near 15 m. calculate the frequency of these radio waves. be sure your answer has the correct number of significant digits.

Explanation:

Step1: Recall the wave speed formula

The speed of light (electromagnetic waves, including radio waves) in a vacuum is \( c = 3.0\times10^{8}\space m/s \). The relationship between speed (\( c \)), wavelength (\( \lambda \)), and frequency (\( f \)) is \( c=\lambda f \). We can rearrange this formula to solve for frequency: \( f=\frac{c}{\lambda} \).

Step2: Substitute the values

We know that \( c = 3.0\times10^{8}\space m/s \) and \( \lambda = 15\space m \). Substituting these values into the formula for frequency: \( f=\frac{3.0\times10^{8}\space m/s}{15\space m} \).

Step3: Calculate the frequency

First, perform the division: \( \frac{3.0\times10^{8}}{15}= 2.0\times10^{7}\space Hz \). The wavelength \( 15\space m \) has two significant digits, and the speed of light is taken as \( 3.0\times10^{8}\space m/s \) (two significant digits for the coefficient), so the result should have two significant digits.

Answer:

\( 2.0\times10^{7}\space Hz \) (or \( 20\space MHz \))