Question

If an electromagnetic wave is described as having a frequency of 3 GHz, what are its period and wavelength (in a vacuum)?

- $3.0 \times 10^9 \textrm{ s}$, 10 cm
- $3.3 \times 10^{-10} \textrm{ s}$, 10 cm
- $3.3 \times 10^{-10} \textrm{ s}$, 10 m
- $3.0 \times 10^9 \textrm{ s}$, 10 m

Final Answer

(b)

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Video Transcript

This is College Physics Answers with Shaun Dychko.
The wave the equation tells us the speed of light equals frequency times wavelength. We can solve this for

*LAMBDA*by dividing both sides by*F*. 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 three gigahertz, which is 3 times 10 to the 9 hertz, which gives away [unclear] of 0.1 meters, which is ten centimeters and that narrows our options down to*A*,*B*or*D*because they all have 10 centimeters. Option*C*is excluded because it has units of meters, actually*D*is also excluded for units of meters. So we've narrowed it down to a or b. So then the next question is, what's the period that's going to be the reciprocal the frequency? So that's 1 over 3 times 10 to the 9 hertz, which is 3.3 times ten to the minus 10 seconds. And so the answer is*B*.