The signal from a 103.9MHz FM radio station reflects off a building 400m away, effectively creating 2 sources of the same signal. ?

You're driving at 60km/h along a road parallel to a line between the station's antenna and the building and located at a perpendicular distance of 6.5km from them. How often does the signal appear to fade when you are driving along the road?

The speed of radio waves is 3.00 x 10^8m/s

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  • 1 month ago
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    Young's equation

    m * lambda / d = y / L

    where

    m is order of antinodal line

    lambda is wavelength 

    d is distance between two sources

    L is distance between screen (in this case screen is road) and sources

    y is perpendicular distance between point P where antinodal line intersects the road and central antinodal line.

    y = L * m * lambda / d

    d= 400m

    L= 6500m

    m = 2

    lambda = c / f =  (3.00 x 10^8) / (103.9 x 10^6) = 2.887 m

    Note that for m=1 we get distance between two adjascent antinodal lines where one is amplifying and the other one is weakening. For distance between points where signal fades we take m=2

    y = 6500 * 2 * 2.887 / 400 = 93.83 m

    v = 60 km/h = 16.67 m/s

    t = 93.83/16.67 = 5.63 s

    Answer: signal fades in intervals 5.63 s

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