Answer to Question #214396 in Electricity and Magnetism for John Mark

Question #214396

(a) What is the wavelength (in meters) of a 93.3 MHz Radio wave frequency? (b) What is the frequency (in Hz) of an x-ray beam with wavelength of 0.0100 nm?


1
Expert's answer
2021-07-06T11:38:09-0400

(a) The wavelength of the radio waves broadcast by an FM radio station is

λ=cfλ = \frac{c}{f}

c is the speed of light in vacuum

c=3×108  m/sf=93.3  MHz=93.3×106  Hzλ=3×10893.3×106=3.21  mc = 3 \times 10^8 \;m/s \\ f= 93.3 \;MHz = 93.3 \times 10^6\;Hz \\ λ = \frac{3 \times 10^8}{93.3 \times 10^6} = 3.21 \;m

(b)

f=cλλ=0.0100  nm=0.01×109  mf=3×1080.01×109=300×1017=3.0×1019  Hzf= \frac{c}{λ} \\ λ= 0.0100 \;nm = 0.01 \times 10^{-9}\;m \\ f = \frac{3 \times 10^8}{0.01 \times 10^{-9}} = 300 \times 10^{17} \\ = 3.0 \times 10^{19}\;Hz


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