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A source and a detector D of high frequ...

A source and a detector ` D` of high frequency waves are `a` distance `d` apart on the ground . Maximum signal is received at `D` when the reflecting layer is at a height `H`. When the layer rises a distance `h` , no signals is detected at `D` . Neglecting absorption in the atmosphere , find the relation between ` d , h , H`, and the wavelength `lambda` of the waves .

Text Solution

Verified by Experts

`(SA + AD) - SD = n lambda` for reinforcement at `D`
Against `(SB + BD) = n lambda + ( lambda)/( 2)` for total annulment at `D`
Subtracting , `(SB + BD) - (SA + AD) = (lambda)/(2)`
` 2( SB - SA) = (lambda)/( 2)`
or ` lambda = 2 sqrt( 4(H + h)^(2) + d^(2)) - 2 sqrt( 4H^(2) + d^(2))`
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