Question

The maximum range for the tropospheric transmission of radio wave of wavelength $3m$ using the transmitting antenna and receiving antenna of heights $100m$ and $60m$ respectively is

• A. $8m$
• B. $800m$
• C. $8km$
• D. $80km$

Answer 1

The correct option is C $8km$

$\lambda =3m$, $H=100m$, $h=60m$
Path difference between direct wave and wave obtained after reflection from the Earth surface is
$\frac{2\pi }{\lambda }\left(\frac{2Hh}{d}\right)+\pi =2\pi$
$\frac{4Hh}{\lambda d}=1$ or $d=\frac{4Hh}{\lambda }$
$⟹d=\frac{4\times 100\times 60}{3}=8\times {10}^{3}m$ or $8km$