Interference

Question

Two identical tuning forks are struck, one a fraction of a second after the other. The sounds produced are modeled by f1(t) = C sin(wt) and f2(t) = C sin(wt + Alpha). The two sound waves interfere to produce a single sound modeled by the sum of these functions

f(t) = C sin(wt) + C sin(wt + Alpha)

a) Use the addition Formula for Sine to show that f can be written in the form f(t) = A sin(wt) + B Cos(wt), where A and B are constants that depend on Alpha.
b) Suppose that C = 10 and Alpha = pi/3. Find constants k and Ö so that f(t) = ksin(wt+Ö)