$A$ carrier wave of peak voltage $12 \,V$ is used to transmit a signal. If the modulation index is $75 \%$, the peak voltage of the modulating signal is (in $\,V$)

In $AM$ transmission,the bandwidth of transmission is $10 \, kHz$ and the carrier frequency is $100 \, kHz$. The sideband frequencies are given by:

The mathematical form of an $AM$ wave is given by $e = 50 (1 + 0.5 \sin(2\pi \times 5 \times 10^{3} t)) \sin(31.4 \times 10^{6} t) \text{ volts}$. Which of the following frequencies is absent in the given $AM$ wave?

Carrier waves are used for communicating signals over long distances because:

$A$ message signal of $12 kHz$ and peak voltage $20 V$ is used to modulate a carrier wave of frequency $12 MHz$ and peak voltage $30 V$. Then,the modulation index is

$A$ transmitting antenna is kept on the surface of the earth. The minimum height of the receiving antenna required to receive the signal in line-of-sight at $4\,km$ distance from it is $x \times 10^{-2}\,m$. The value of $x$ is (Let radius of earth $R = 6400\,km$).