Two towers on top of two hills are 40 km apart.The line joining them passes 50 m above a hill halfway between towers. What is the longest wavelength of radiowaves which can be sent between the towers without appreciable diffraction ?

Asked by Kb Aulakh | 27th Apr, 2015, 11:10: PM

Expert Answer:

Given the distance between the two towers = 40 km
We know that for distances smaller than Fresnels distance(ZF) , spreading due to diffraction is smaller as compared to the size of the waves. 
But the hill is half way between the tower so distance upto which much of diffraction will not be observable should be 40/2 = 20km = 20,000m
We know that Fresnels disatnce is the minimum distance a beam of light can travel before its deviation from straight line path due to diffraction becomes significant.
Hence ZF = 20,000 m
For the hill not to obstruct the spreading radio beam, the radial spread of the beam over the hill 20 km away must not exceed 50 m.
begin mathsize 12px style We space know space that comma space space straight Z subscript straight F space equals straight a squared over straight lambda where space straight a equals space 50 space straight m straight Z subscript straight F equals space 20 comma 000 space straight m Therefore space straight lambda space equals straight a squared over straight Z subscript straight F straight lambda space equals space fraction numerator 50 squared over denominator 20 comma 000 end fraction equals 0.125 space straight m end style
Therefore the longest wavelength of radiowaves which can be sent between the towers without appreciable diffraction = 0.125 m

Answered by Jyothi Nair | 28th Apr, 2015, 08:45: AM