Consider a narrow band signal, propagating in a lossless dielectric medium $$(\varepsilon_r=4,\mu_r=1)$$, with phase velocity $$v_p$$ and group velocity $$v_g$$. Which of the following statement is true? ($$c$$ is the velocity of light in vacuum.)

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?

Consider a rectangular coordinate system $(x, y, z)$ with unit vectors $a_x, a_y$ and $a_z$. A plane wave traveling in the region $z \geq 0$ with electric field vector $E=10 \cos \left(2 \times 10^8 t+\beta z\right) a_y$ is incident normally on the plane at $z=0$, where $\beta$ is the phase constant. The region $z \geq 0$ is in free space and the region $z<0$ is filled with a lossless medium (permittivity $\varepsilon=\varepsilon_0$ permeability $\mu=4 \mu_0$, where $\varepsilon_0=8.85 \times 10^{-12} \mathrm{F} / \mathrm{m}$ and $\mu_0=4 \pi \times 10^{-7} \mathrm{H} / \mathrm{m}$ ). The value of the reflection coefficient is