question_answer

Two radio antennas separated by 300 m are simultaneously broadcasting signals of same wavelengths.

A car is moving over a parallel path at a distance of 1000 m from line joining antennas as shown below.

At 400 m from the centre line of antenna, a radio fitted in car registers a second minima. Wavelength of transmission is around

A) 110m

B)                    45m

C) 65 m                

D) 55 m

Correct Answer: D

Solution :

As distance between antennas is large, we are not using approximation \[\theta \approx \sin \theta \approx \tan \theta \]

Now, from figure

\[\tan \theta =\frac{400}{1000}=0.4\]

So, \[\sin \theta =\frac{4}{\sqrt{116}}\]

Now, wavelength, \[\lambda =\frac{d\sin \theta }{m}\]

\[=\left( \frac{300\times \frac{4}{\sqrt{116}}}{2} \right)=55.65m\]

So,\[\lambda \approx 55m\]