Is "The Wave" at the stadium a transverse wave or a longitudinal wave?
1. Transverse
2. Longitudinal
3. Neither
Note:
* Correct Answer: A
A sound wave is a:
1. transverse wave
2. longitudinal wave
3. it's not a wave at all
Note:
* Correct Answer: B
A wave on a stretched drum head is an example of a:
1. transverse wave
2. longitudinal wave
3. it's not a wave at all
Note:
* Correct Answer: A
## Announcements
* Quiz this Friday (Maxwell Ampere + Poynting Vector)
* Determine the electric and magnetic field in a situation where there is a displacement current
* Discuss the direction of the Poynting vector and how it relates to conservation of energy
The electric field for a plane wave is given by:
$$\mathbf{E}(\mathbf{r},t) = \mathbf{E}_0e^{i(\mathbf{k}\cdot\mathbf{r} - \omega t)}$$
The vector $\mathbf{k}$ tells you:
1. The direction of the electric field vector.
2. The speed of the traveling wave.
3. The direction the plane wave moves.
4. A direction perpendicular to the direction the plane wave moves
5. None of these/MORE than one of these/???
Note:
* Correct Answer: C
The electric field for a plane wave is given by:
$$\mathbf{E}(\mathbf{r},t) = \mathbf{E}_0e^{i(\mathbf{k}\cdot\mathbf{r} - \omega t)}$$
Suppose $\mathbf{E}_0$ points in the $+x$ direction.
Which direction is this wave moving?
1. The $x$ direction.
2. The radial ($r$) direction
3. A direction perpendicular to both $\mathbf{k}$ and $\mathbf{x}$
4. The $\mathbf{k}$ direction
5. None of these/MORE than one of these
Note:
* Correct Answer: D
A wave is moving in the $+z$ direction:
$$f(x, y, z, t) = Re\left[A e^{i(kz – \omega t + \delta)}\right]$$
The value of $f$ at the point $(0,0,z_0, t)$ and the point at $(x, y, z_0 , t)$ are related how?
$f_1 = f (0,0,z_0 , t)$ vs. $f_2 = f(x, y, z_0 , t)$
1. $f_1 = f_2$ always
2. $f_1 >$ or $<$ or $= f_2$ depending on the value of $x,y$
<img src="./images/two_points_plane_wave.png" align="center" style="width: 500px";/>
Note:
* Correct Answer: A
The electric field of an E/M wave is described by:
$$\mathbf{E} = E_0\sin\left(kx-\omega t\right)\hat{\mathbf{y}}$$
What is the direction of the magnetic field?
1. $+x$
2. $+y$
3. $–x$
4. $+z$
5. $-z$
Note:
* Correct Answer: D
You have this solution to Maxwell's equations in vacuum:
$$\widetilde{\mathbf{E}}(x,y,z,t) = \widetilde{\mathbf{E}}_0 \exp\left[i\left(\mathbf{k}\cdot\mathbf{r} - \omega t\right)\right]$$
If this wave travels in the $y$ direction, is polarized in the $x$ direction, and has a complex phase of 0, what is the $x$ component of the physical wave?
1. $E_x = E_0 \ cos\left(kx-\omega t\right)$
2. $E_x = E_0 \ cos\left(ky-\omega t\right)$
3. $E_x = E_0 \ cos\left(kz-\omega t\right)$
4. $E_x = E_0 \ cos\left(k_x x+k_y y-\omega t\right)$
5. Something else
Note:
* Correct Answer: B
The electric fields of two EM waves in vacuum are both described by:
$$\mathbf{E} = E_0 \sin(kx-\omega t)\hat{y}$$
The "wave number" $k$ of wave 1 is larger than that of wave 2, $k_1 > k_2$. Which wave has the larger frequency $f$?
1. Wave 1
2. Wave 2
3. impossible to tell
Note:
* Correct Answer: A
* Same speed and thus wavelength of 1 is smaller, so frequency is higher