Question

Light, radiant heat (infrared radiation), X rays, and radio waves are all examples of traveling electromagnetic waves. Electromagnetic waves comprise combinations of electric and magnetic fields that are mutually compatible in the sense that the changes in one generate the other. The simplest form of a traveling electromagnetic wave is a plane wave. For a wave traveling in the x direction whose electric field is in the y direction, the electric and magnetic fields are given by Ē = E, sin(kx – wt) Î B = B, sin(kx - wt) k Since linear polarization is defined by the direction of the electric field vector, this wave is linearly polarized in the y direction. 1. For a given wave, what are the physical variables to which the wave responds? Mark all that apply. O X Ok O E Ot 0 0 OBO 2. Which of the parameters determine the characteristics of the wave? Mark all that apply. O XO kO EO Ot 0 0 OBO 3. What is the wavelength of this wave? Show your work or explain in words. 4. What is the period T of this wave? Show your work or explain in words. 5. What is the velocity v of this wave? Show your work or explain in words. 6. Which part of the equation for the electric field do we call "the phase"? Explain in words. 7. What is the mathematical expression for the electric field at the point (x = 0, y = 0, 2) at time t?

Answer 1

For a given wave, what are the physical variables to which the wave responds? Mark all that apply.

The physical variables to which the wave responds is the displacement given by x and the time in which it performs the displacement given by t.

Which of the parameters determine the characteristics of the wave?

The parameters that determine the characteristics of the wave are the displacement x, the time t, the angular wave number k and the angular frequency $\omega$ .

What is the wavelenght $\lambda$ of this wave?

The wavelength $\lambda$ is related to the angular wave number k by the following equation:

$k=\frac{2\pi }{\lambda }$

The wavelength is given by:

$\lambda =\frac{2\pi }{k}$

What is the period T of this wave?

The period T of the wave is given by:

$T=\frac{1}{f}$

where f is the frequency of the wave. We can relate the frequency of wave f with the angular frequency $\omega$ of wave by the following equation:

w = 2nf = f =

replacing the frequency f in the equation of the period, we obtain:

3 =||

What is the velocity v of this wave?

The velocity v of the wave is given by:

v = c = AS = ( ) =

Which part of the equation for the electric field do we call the phase?

The phase of the wave is everything in parentheses:

Phase = (kr - wt)