FM radio station KRTH in Los Angeles broadcasts on an assigned frequency of 101

Question

FM radio station KRTH in Los Angeles broadcasts on an assigned frequency of 101 MHz with a power of 50,000 W. (a) What is the wavelength of the radio waves produced by this station? (b) Estimate the average intensity of the wave at a distance of 10.5 km from the radio transmitting antenna. Assume for the purpose of this estimate that the antenna radiates equally in all directions, so that the intensity is constant over a hemisphere centered on the antenna. (c) Estimate the amplitude of the electric field at this distance.

Explanation / Answer

a)

The wavelength of the wave is given by

    speed of the wave(v) =Frequency of the wave(f) * wavelength of the wave (lamda)

Then lamda = v/f =3*108m/s/101 MHz ==3*108m/s/101*106Hz =2.90m

b)

The intensity of the electromagentic wave is

I =P/4pir2 =50000W/4*3.14*(10.5*103)2 =3.610*10-5W/m2

c)

We know that

Iavg =eocEo2/2

Then Eo =Sqrt(2Iavg/eoc) =Sqrt(2*3.610*10-5W/m2/8.85*10-12*3*108)

                                                  =0.165V/m

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