03.Reflection and Transmission of Waves at a Boundary

 Reflection and Transmission of Waves at a Boundary

 An incident wave travelling along string meets discontinuity in Impedance at x=0,

some part of incident wave will be reflected and part of it will be transmitted.

• Tension(T) is same on both side of x=0.
• Linear density is different on both side P1 & P2.
• Velocity is different on both side c1 & c2.
• So, Impedance will be different on both side.
• Assume amplitude A1 of incident wave with velocity c1 and displacement yi .
• and B1 amplitude of reflected wave with velocity c1 (as same) and displacement yr .
• and A2 amplitude  of transmitted wave with velocity c2 and displacement y t.

Conditions

1. A Geometrical condition that the displacement is the same immediately to the left and right of x=0, so that no discontinuity of displacement.
   
    
    
   2. A Dynamical condition that there is a continuity of the transverse force at x=0 so a continuous slope.