A truck driver is broadcasting at a frequency of 27.335 MHz with a CB (citizen\'

Question

A truck driver is broadcasting at a frequency of 27.335 MHz with a CB (citizen's band) radio. Determine the wavelength of the electromagnetic wave being used. The speed of light is c = 2.9979 times 10^8 m/s. Magnetic resonance imaging, or MRI, and positron emission tomography, or PET scanning, are two medical diagnostic techniques. Both employ electromagnetic waves. For these waves, find the ratio of the MRI wavelength (frequency 5.40 times 10^7 Hz) to the PET scanning wavelength (frequency = 1.23 times 10^20 Hz). When we look at the star Polaris (the North Star), we are seeing it as it was 680 years ago. How far away from us (in meters) is Polaris?

Explanation / Answer

1)

wavelength = velocity / frequecy

lambda = c/f

lambda = (2.9979 x 10^8 m/s) / (27.335 x 10^6 Hz)

lambda = 10.9673 m

2)

C = fL

3 x 10^8 = (5.4 x 10^7)L

L= 5.555 m

C = fL

3 x 10^8 = (1.23 x 10^20)L

L= 2.439 x 10^-12 m

ratio = 5.555 m / (2.439 x 10^-12 m) = 2.277 x 10^12

3)

v = c/t

d = ct

here c = 3 x 10^8 m/s

t = 680 years = 2.144 x 10^10 sec

d = 3 x 10^8 m/s x 2.144 x 10^10 s

d = 6.432 x 10^18 m

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