I have no idea what this is asking, please give an explanation. 2. A wave of amp
ID: 1260055 • Letter: I
Question
I have no idea what this is asking, please give an explanation.
2. A wave of amplitude A is reflected from a barrier at normal incidence. 1f the amplitude of the reflected wave is B, the reflection coefficient of the barrier is defined by r = B/A. It is difficult to measure A or B directly, but relatively easy to measure the amplitude of the standing wave which forms in front of the barrier. The maximum and minimum amplitudes, a and Beta, of the standing wave are given by . . . . alpha = A+B .? Beta = A-B . Find an expression, for the variance of r, sigma r^2 in terms of the known quantities alpha , beta and their variances Sigma alpha^2, sigma r^2. You may assume that the measurements of alpha ,beta are independent so that sigma alpha Beta ^2= 0.Explanation / Answer
alpha a = A + B
beta b= A - B
A = [a + b ] /2
B = [a - b] / 2
r = B/A = [a-b] / [a + b}
mean amplitude = a + b /2 = A
variance = [a - mean ]^2 / 2 = [a - A]^2 / 2 = [[2a - a-b]/2]^2 / 2 = [a-b]^2 / 8
variance for b = [b - mean ]^2 / 2 = [b - A]^2 / 2 = [[2b - a-b]/2]^2 / 2 = [a-b]^2 / 8
as variance for a and b are same thus
variance ab = variance a - variance b = 0