Question

1. Using the notes on specific impedance to find reflection and transmission coefficients (R and T), prove that: R = (Z - Z) / (Z2 +Z1) and T = 22 / (22 + Zi) 9:(x,t) = Ae/(wt-K2X) h(x, t) = Bel(wt+k;*) 92(x, t) = Ae/(wt-(2x) where c), and ca the wavespeeds of strings 1 and 2.

Answer 1

Pg No - 0 Solution - Given data: to The Specific impedance find Reflection Notes on and transmission coefficient R = (2, -22) / (22 +21) And T= 22, / (22+2) 9, (t) = Ael(wt- kıx) = UR 92 (x, t) - Be I Cwt + kix) = 46 b, (x, t) - Red (cot - k2x) = 4 there, The Reflection and Transmission :- Incidenct Reflection and Transmission waves, → Imposing Boundary condition, continunity at x=0 Now, Y, Ct) + 4y(t) = 44 (t) – O Fan

Pg No - 6 for the Boundary Eqh a haver de cont. 03 ((t.)+ 4H). - (-4, (+) +w\CH] Tidy Cot) - To You (+ .]0-140) f=cu) - + 4C) other words :- - 15,40€) + Ty X, (p) + Win 24 (0)=0 Since, A function whose de fermation Vanishes must be Constant. Becomes it's ► ) [+y;lt) + 45 CH)) --TA YA(+) + Cout" - Nao Substituting in Eqn 0 in Egh ® 1 [+ visted + 9,ce) ) [9928+4,60] + ) y = (1 ) 4:2

y - Telu »lly = T/ + 10/02 By using Equation 6 the transmitted wave The Relevent amplitude also are has the Same Shope the main useful formel 2 = /v , 22 = T2 / V2 Vo = 21-22 . 2,tz, Substituting Back to Equation o Ve= 221 Zitza Vr = R41 and 4 += Tyi & The Reflection coefficient R= 21 - 22 ZitZa. . The Transmission Collictent T = 22, Zitza