D.

4 beats per second with intensity ratio 81:1 between waxing and waning

Given, y₁ = 4sin 600π t and y₂ = 5 sin 608πt
Comparing with general equation
y = a sin 2πft
 we get, f₂ = 300 Hz and f₂ 304 Hz
Number of beats = f₂-f₁ = 4s^-1

A.

perpendicular to the diameter

When the point is on the diameter and away from the centre of hemisphere which is charged uniformly and positively, the component of electric field intensity parallel to the diameter cancel out. So the electric field is perpendicular to the diameter.

D.

100

Let intensity of sound be I and I'. Loudness of sound initially

$$\begin{gathered} {\mathrm{\beta }}_1 = 10 \log \left(\frac{\mathrm{I}}{{\mathrm{I}}_{\mathrm{o}}}\right) \\ {\mathrm{\beta }}_2 = 10 \log \left(\frac{\mathrm{I}\text{'}}{{\mathrm{I}}_{\mathrm{o}}}\right) \end{gathered}$$

β₂ - β₁ = 20

$\therefore 20 = 20 \log \left(\frac{\mathrm{I}\text{'}}{\mathrm{I}}\right)$

∴ I' = 100 I

D.

(9/4) fold

We know that a phase change of π occurs when the reflection takes place at the boundary of the denser medium. This is equivalent to a path difference of λ/2.

Therefore, Total phase difference = π -π = 0

Thus, the two waves superimpose in phase.

Resultant,

$$\begin{gathered} \mathrm{Resultant} \mathrm{amplitude} = \sqrt{\mathrm{I}} + \sqrt{\left(\frac{\mathrm{I}}{4}\right)} = \frac{3}{2}\sqrt{\mathrm{I}} \\ \mathrm{Resultant} \mathrm{amplitude} = {\left(\frac{3}{2}\sqrt{\mathrm{I}}\right)}^2 = \frac{9}{4} \mathrm{I} = \frac{9}{4} \mathrm{fold} \end{gathered}$$ 

A.

5 MHz

The ionosphere extends from a height of 80 km to 300 km. The refractive index of ionosphere is less than its free space value. That is, it behaves as a rarer medium. As we go deep into the ionosphere, the refractive index keeps on decreasing. The bending of beam (away from the normal) will continue till it reaches critical angle after which it will be reflected back. The different points on earth receive signals reflected from different depths of the ionosphere. There is a critical frequency f, (S to 100 MHz) beyond which the waves cross the ionosphere and do not return back to earth.