For an amplitude modulated wave,the maximum and minimum amplitudes are found to be $10 \ V$ and $2 \ V$ respectively. Then the modulation index is

In an $AM$ wave,the carrier power is given by:

$A$ message signal of frequency $10 kHz$ and peak voltage of $15 V$ is used to modulate a carrier frequency of $1 MHz$ and peak voltage of $30 V$. Determine the modulation index.

In a communication system,the range for line-of-sight propagation on Earth is $d$ for an antenna height of $h$. If $h$ is doubled,then the new range is:

$A$ transmitting antenna can cover an area of $6.4\pi \times 10^9 \ m^2$ when used for broadcasting. If the signal is transmitted to another antenna,which is at a distance of $100 \ km$ from this antenna,what should be the minimum height of the receiving antenna for satisfactory communication in line-of-sight mode (in $m$)? (Assume the radius of the Earth $R = 6400 \ km$)

$A$ $TV$ transmitting antenna is $128 \ m$ tall. If the receiving antenna is at the ground level,the maximum distance between them for satisfactory communication in line-of-sight mode is (radius of the earth $R_e = 6.4 \times 10^6 \ m$):