Interference/Diffraction Question

1. The problem statement, all variables and given/known data

a) Given a source that emits in all directions at a frequency ##f=2.4 MHz##and power ##P = 100 W##, suppose there are 2 sources (one above and one below) separated by a distance of ##d= 200 m##. Plot the graph of the intensity as a function of angle on a circle of radius ##10,000 m## around the two sources, including interference effects to calculate the net intensity.

b) If the phase of the lower source is swept from ##\phi= +\frac{\pi}{10}## to
##\phi= -\frac{\pi}{10}## with respect to the upper source, plot the angle where the ##m=0## interference peak is found as a function of the phase difference between the upper and lower source.

c) 20 sources are arranged on the radius ##200 m## apart on the radius of the ##10 km## circle. What is the intensity at the center of the circle?

2. Relevant equations

##I=\frac{P}{4\pi R^2}##
##I(\theta) = I_0 (\cos{\frac{\pi d \sin{\theta}}{\lambda}})^2##
From my textbook, ##\phi = \frac{2 \pi d \sin{\theta}{\lambda}##

3. The attempt at a solution

For part a), I apply the interference equation above and plot as a function of theta. Or am I going about this all wrong?

For part b), I don’t have much clue. The above equation for phase?

For part c), The intensity from one source is ##I = \frac{100 W}{4 \pi (10000)^2}## so the total intensity is just ##20^2 I##

http://ift.tt/OtgtdS

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