# 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

Relevance

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