$A$ speech signal of $3 \text{ kHz}$ is used to modulate a carrier signal of frequency $1 \text{ MHz}$ using amplitude modulation. The frequencies of the sidebands will be:

The size of the antenna required for a carrier wave of frequency $3 \text{ MHz}$ is: (in $\text{ m}$)

$A$ message signal is super-imposed with a carrier signal. The resulting modulating signal $C_m(t)$ is given by $C_m(t)=A_1 \sin \left(\omega_1 t\right)+A_2 \sin \left(\omega_2 t\right)-A_2 \sin \left(\omega_3 t\right)$,where $\omega_2 < \omega_1 < \omega_3$. The modulation index and the angular frequency of the message signal respectively,are

$A$ $..........$ is used in the receiver section to reduce the magnitude of signals.

Given the electric field of a complete amplitude modulated wave as $\vec E = \hat i E_c (1 + \frac{E_m}{E_c} \cos \omega_m t) \cos \omega_c t$,where the subscript $c$ stands for the carrier wave and $m$ for the modulating signal. The frequencies present in the modulated wave are:

$A$ person tries to broadcast with the same antenna both the signals at $10^7 \,Hz$ and $10^6 \,Hz$. If the receiver at some distance has to receive an equal strength for both the frequencies, then the broadcaster has to approximately increase the signal strength at $10^6 \,Hz$ to $10^7 \,Hz$ by