The waves from a radio station can reach a home receiver by two paths. One is a

Question

The waves from a radio station can reach a home receiver by two paths. One is a straightline path from transmitter to home, a distance of 29.4 km. The second path is by reflection from the ionosphere (a layer of ionized air molecules near the top of the atmosphere). Assume this reflection takes place at a point midway between receiver and transmitter and that there are no phase changes on reflection. If the wavelength broadcast by the radio station is 286 m, find the minimum height h of the ionospheric layer that produces destructive interference between the direct and reflected beams. Answer in units of km.

Explanation / Answer

here

the signal that bounced off the ionosphere would travel 286 / 2 = 143 m further than the direct signal = 29400 + 143=29543 m

using trigonometry, draw a right angled triangle with base = 29400/2 = 14700m, and a hypotenuse of 29543/2 = 14771.5 m

then

h = sqrt( 14771.5^2 - 14700^2)

h = sqrt(2107212)

h = 1451.62 m

so the height of ionosoheric layer is 1451.62 m

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