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If an electromagnetic wave is described as having a frequency of 3 GHz, what are its period and wavelength (in a vacuum)?
  1. $3.0 \times 10^9 \textrm{ s}$, 10 cm
  2. $3.3 \times 10^{-10} \textrm{ s}$, 10 cm
  3. $3.3 \times 10^{-10} \textrm{ s}$, 10 m
  4. $3.0 \times 10^9 \textrm{ s}$, 10 m
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OpenStax College Physics for AP® Courses Solution, Chapter 24, Problem 1 (Test Prep for AP® Courses) (0:52)

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This is College Physics Answers with Shaun Dychko. The wave equation tells us the speed of light equals frequency times wavelength. We can solve this for <i>lambda</i> by dividing both sides by <i>F</i>. And so the wavelength is speed of light divided by frequency. So it’s 3 times 10 to the 8 meters per second divided by 3 gigahertz, which is 3 times 10 to the 9 hertz, which gives a wavelength of 0.1 meters, which is 10 centimeters and that narrows our options down to <i>A</i>, <i>B</i> or <i>D</i> because they all have 10 centimeters. Option <i>C</i> is excluded because it has units of meters, actually <i>D</i> is also excluded for units of meters. So we've narrowed it down to <i>A</i> or <i>B</i>. So then the next question is, what's the period that's going to be the reciprocal of frequency? So that's 1 over 3 times 10 to the 9 hertz, which is 3.3 times 10 to the minus 10 seconds. And so the answer is <i>B</i>.