Find the modulation index of an $AM$ wave having $8\,V$ variation where maximum amplitude of the $AM$ wave is $9\,V$.

Audio signals cannot be transmitted directly over long distances because:

In an amplitude modulated signal,the maximum amplitude is $15 V$ and the minimum amplitude is $5 V$. The amplitude of the modulating wave will be (in $V$)

$A$ 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 heights of the transmitting and receiving antennas are $33.8 \ m$ and $64.8 \ m$ respectively. The maximum distance between the antennas for satisfactory communication in a line of sight mode is (Radius of the earth $= 6400 \ km$) (in $km$)

The height of the transmitting antenna is $180\,m$ and the height of the receiving antenna is $245\,m$. The maximum distance between them for satisfactory communication in line of sight will be .......... $km$ (given $R = 6400\,km$).