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

Question

(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?

Answer 1

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

$λ = \frac{c}{f}$

c is the speed of light in vacuum

$c = 3 \times 10^8 \;m/s \\ f= 93.3 \;MHz = 93.3 \times 10^6\;Hz \\ λ = \frac{3 \times 10^8}{93.3 \times 10^6} = 3.21 \;m$

(b)

$f= \frac{c}{λ} \\ λ= 0.0100 \;nm = 0.01 \times 10^{-9}\;m \\ f = \frac{3 \times 10^8}{0.01 \times 10^{-9}} = 300 \times 10^{17} \\ = 3.0 \times 10^{19}\;Hz$