1
GATE ECE 2022
MCQ (More than One Correct Answer)
+1
-0.33

Consider the following wave equation,

$${{{\partial ^2}f(x,t)} \over {\partial {t^2}}} = 10000{{{\partial ^2}f(x,t)} \over {\partial {x^2}}}$$

Which of the given options is/are solution(s) to the given wave equation?

A
$$f(x,t) = {e^{ - {{(x - 100t)}^2}}} + {e^{ - {{(x + 100t)}^2}}}$$
B
$$f(x,t) = {e^{ - (x - 100t)}} + 0.5{e^{ - (x + 1000t)}}$$
C
$$f(x,t) = {e^{ - (x - 100t)}} + \sin (x + 100t)$$
D
$$f(x,t) = {e^{j100\pi ( - 100x + t)}} + {e^{j100\pi (100x + t)}}$$
2
GATE ECE 2016 Set 2
+1
-0.3
Let the electric field vector of a plane electromagnetic wave propagating in a homogenous medium be expressed as $$E = \widehat x{E_x}\,{e^{ - j\left( {wt - \beta z} \right)}},$$ , where the propagation constant $$\beta$$ is a function of the angular frequency $$\omega$$. Assume that $$\beta \left( \omega \right)$$ and $${E_x}$$ are known and are real. From the information available, which one of the following CANNOT be determined?
A
The type of polarization of the wave.
B
The group velocity of the wave.
C
The phase velocity of the wave.
D
The power flux through the z = 0 plane.
3
GATE ECE 2016 Set 3
+1
-0.3
If a right-handed circularly polarized wave is incident normally on a plane perfect conductor, then the reflected wave will be
A
right-handed circularly polarized
B
left-handed circularly polarized
C
elliptically polarized with a tilt angle of 450
D
horizontally polarized
4
GATE ECE 2015 Set 2
+1
-0.3
The electric field of a uniform plane electromagnetic wave is $$\vec E = \left( {{{\overrightarrow a }_x} + j4{{\overrightarrow a }_y}} \right)\exp \left[ {j\left( {2\pi \times {{10}^7}t - 0.2z} \right)} \right]$$\$

The polarization of the wave is

A
right handed circular
B
right handed elliptical
C
left handed circular
D
left handed elliptical
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