FM radio station KRTH in Los Angeles broadcasts on an assigned frequency of 101
ID: 1699043 • Letter: F
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 10.8 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) ?f=c, where ? is the wavelength we're looking for and c is the speed of light (3.0x10^8m/s) ?=c/f -->?=[3.0x10^8]/[101x10^6] //MHz is 10^6 Hz ?=2.97m -->you should check my arithmetic, which sucks most of the time. (b) Equation: You will see I = P/A in your book and online. --> Since the electric field only stores 1/2 that radiation energy emitted, however, we have to divide by two. I=P/2A. 50,000/ [2pi x 35800^2] = 6.21x10^-6 W/m^2 (c) E°(r)=sqrt[ (P/(2*pi*c*e))/r ] --> P is power and e is the permittivity of free space constant (8.85x10^-12 Nm^2/C^2). E° is the amplitude of the electric field (what we're trying to find). I got 83.7 V/m. But...you should go over that. I really suck at arithmetic. I'm not even kidding. They made me do 1st grade twice and 5th grade math three times.
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