2.1 Introduction
2.2 Generation of Electromagnetic Waves
2.2.1 Speed of Electromagnetic Waves
2.2.2 Direction of Propagation of Electromagnetic Waves
2.2.3 Doppler Effect of Electromagnetic Waves
2.3 The Electromagnetic Spectrum
2.4.1 Energy Carried by Electromagnetic Waves
2.4.2 Radiation Pressure
2. Summary
Unit 2 - Multiple Choice - Electromagnetic Waves Questions
Unit 2 - Multiple Choice - Electromagnetic Waves Answers
Unit 2.1 Multiple Choice Extended Questions - Waves
Unit 2.1 Multiple Choice Extended Answers-Waves
 

Unit 2 Electromagnetic Waves

2.2 Propagation of Electromagnetic Waves

2.2.3 Doppler Effect of Electromagnetic Waves

The normal Doppler shift for waves such as sound which move with velocities v much less than c is given by the expression:

fobserved = fsource{V/[VVs]} (source moving and stationary observer)

A positive value is used for motion of the source away from the observer.

Light waves travel in empty space so the Doppler effect for light is analyzed in terms of the motion of the source relative to the listener who is always considered to be at rest. If the source is moving away from the listener, its velocity v is positive, but if it is moving toward the listener, then the v is negative. The speed of light c is always considered positive.

At non-relativistic speeds (c >> Vs we calculate Vrelative using the formula

fobserved = fsource{c/[c±Vs]}

 

At relativistic speeds we calculate Vrelative using the formula

Vrelative = [Vs + Vp] /{[1 + VsVp] /c2}

so adjusting the equation fobserved = fsource{V/[V±Vs]}

we get fobserved = fsource{1/√[1-β2]} where β = Vs/c

If the source is moving away from the observer then fobserved < fsource.

If the source is moving towards the observer then fobserved > fsource - In the visible spectrum we get a shift to the red end of the spectrum called a red shift and

If the source is moving towards the observer then fobserved > fsource -In the visible spectrum we get a shift to the blue end of the spectrum called a blue shift.

Wavelength is easier to measure than frequency so we often work with wavelength.

Example 1: A galaxy is moving away from the Earth at 2.6x107ms-1. Calculate the wavelength and frequency change of a 650 nm line in its spectrum. Take c = 3x108ms-1.

fsource = c/λ

fsource = 4.6x1014Hz

fobserved = fsource{c/[c±Vs]}

fobserved = 4.6x1014Hz{(3x108ms-1)/[(3x108ms-1)+(2.6x107ms-1)]}

fobserved =4.2x1014Hz

λobserved = c/fobserved

λobserved = 709 nm

The frequency has shifted from red to infrared.

Example 2: A distant galaxy is moving away from us at approximately 5x107ms-1 and we approximate the speed of light as c = 3x108ms-1. (a) What is the resulting wavelength of the Hydrogen spectral line of λ = 434 nm? (b) what would be the shift if the galaxy was moving towards earth?

(a) fsource = c/λ

fsource = 6.91x1014Hz

fobserved = fsource{c/[c±Vs]}

fobserved = 6.91x1014Hz{(3x108ms-1)/[(3x108ms-1)+(5.0x107ms-1)]}

fobserved =5.92x1014Hz

λobserved = c/fobserved

λobserved = 507 nm

The frequency has shifted from violet to green.

(b) fobserved = fsource{c/[c±Vs]}

fobserved = 6.91x1014Hz{(3x108ms-1)/[(3x108ms-1)-(5.0x107ms-1)]}

fobserved =8.29x1014Hz

λobserved = c/fobserved

λobserved = 362 nm

The frequency has shifted from violet to ultraviolet.

     
Concept by Kishore Lal. Programmed by Kishore Lal... Copyright © 2015 Kishore Lal. All rights reserved.