Question
(a) What is the wavelength of 100-MHz radio waves used in an MRI unit? (b) If the frequencies are swept over a
range centered on 100 MHz, what is the range of wavelengths broadcast?
Final Answer
Solution video
OpenStax College Physics, Chapter 24, Problem 22 (Problems & Exercises)
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Video Transcript
This is College Physics Answers with Shaun Dychko. An MRI machine uses radio waves with a frequency of 100 megahertz, which is 100 times 10 to the 6 hertz and the question in part (a) is what is the wavelength of this radio wave? So the wave equation says that the speed of the wave, which is the speed of light in this case equals the frequency multiplied by the wavelength and we can solve for λ by dividing both sides by f. So the wavelength then is the speed of light divided by its frequency that's 2.998 times 10 to the 8 meters per second divided by 100 times 10 to the 6 hertz, which is 3.00 meters. And part (b) says if the frequencies are swept over a plus or minus one megahertz range, what is the range of wavelengths? So in the first case, we have the speed of light divided by the first frequency which we'll take to be 100 megahertz plus 1 so 101 times 10 to the 6 hertz and that is 2.97 meters and then the other end of the range for the wavelength is speed of light divided by the lowest possible frequency, which is 100 minus 1 times 10 to the 6 hertz and that works out to 3.03 meters. So the range of wavelengths is anything between 2.97 meters or less than 3.03 meters.