Question

Please Help!!!!!

2) Using the known relation between the speed of light, wavelength, and frequency, calculate the wavelength (in meters) of the following electromagnetic waves (kHz=103 s-1, MHz=106 s-1, GHz=109 s-1):

a) Ultra-low frequency communications (submarines) at 3kHz

b) a typical microwave oven at 3GHz Show all steps!!!!!

3) The 21cm (wavelength=0.21 meters) spectral line of neutral hydrogen is one of the most important and observationally useful electromagnetic radiation in galactic astronomy and cosmology. Its detection, as well as observations of its Doppler shift contribute to astronomers being able to deduct the structure, movement, and mass of galaxies and galaxy clusters throughout the universe.


If you were to devise a simple radio antenna capable of detecting the 21cm line, what frequency should it be tuned to? Show all steps of your calculations!!!!!

Answer 1

a) A 3 kHz wave has a wavelength of 1 × 10⁵ m.

fλ = c

λ = c/f = 2.998 × 10⁸ m·s⁻¹/3 × 10³ s⁻¹ = 1 × 10⁵ m

b) A 3 GHz wave has a wavelength of 0.10 m.

λ =c/f = 2.998 × 10⁸ m·s⁻¹/3 × 10⁹ s⁻¹ = 0.10 m

c) You should tune an antenna for 21 cm radiation to a frequency of 1.4 GHz.

f = c/λ = 2.998 × 10⁸ m·s⁻¹/0.21 m = 1.4 × 10⁹ s⁻¹ = 1.4 GHz