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