12. Quarter wave matching layer calculation: Let there be three different layers of media, with respective acoustic impedances z1, 22 and 23 with boundaries located at x=0 and x = L. Let p = Pe- and p = Pe***), where k = w/c is the wave number, P = Ae) and P = Be(+) and finally p. -Pet- Continuity of normal specific acoustic impedance implies that at x = 0: P+P, Z A + B P-P, ZA-B and at x = L: Ae-+ Be Ae--Bel Z3 Z2 a) As an optional exercise, use the cosine, sine and exponential identities to show that the intensity transmission coefficient, TI, can be written in the following form: [10pts extra credit] 4 2+ + ( + ) coskL + | + (2/23 + 2123) sinkL T = b) If kL (2n-1 2n 1), what is Tr? (2 pts) Z123 Z1Z3 Z2 c) If =3 (the geometric mean of z and z3), what is T? (2 pts)