Consider a group of waves that have a distribution of k values such that the net signal is given by
y = acos(kx) + acos(k+kx) + ... + acos(k+n-1kx) (5)
a. What is k, the average k value in the band?
b. What is the bandwidth k?
c. In the limit that k is small, show that y can be written as a sinc function.
d. In this same limit, what is the spatial width of the wave group x in terms of k? Hint: Find the first zero of the sinc function.