Question

A radio station operating at a frequency $1500K{H}_z$ has two vertical dipole antennas spaced $400m$ apart oscillating in phase. In which directions are the intensity greatest?

• A. $0,\pm {30}^0,\pm {90}^0$
• B. $0,\pm {30}^0,\pm {60}^0$
• C. $0,\pm {45}^0,\pm {90}^0$
• D. $\pm {30}^0,\pm {60}^0,\pm {90}^0$

Answer 1

The correct option is A $0,\pm {30}^0,\pm {90}^0$

We have $\lambda =\frac{c}{f}=\frac{3\times {10}^{8}m/s}{1500\times {10}^3{s}^{-1}}=200m$

max: $dsin\theta =m\lambda ⟹sin\theta =\frac{m\lambda }{d}=\frac{m\left(200\right)}{400}=\frac{m}{2}$

$⟹m=0⟹\theta =0$
Hence $m=\pm 1⟹\theta =\pm {30}^o,m=\pm 2⟹\theta =\pm {90}^o$

So, the answer is option (A).