a) A Transverse waves propagating on a stretched string encounter another string of different characteristic impedance. (i) Write down the equations of particle displacement due to the incident, reflected and transmitted waves. (ii) Specify the boundary conditions and (iii) use these to obtain expressions for reflection and

transmission amplitude coefficients.

When a transverse wave propagates on a stretched string and encounters a second string with different characteristic impedance, the wave undergoes reflection and transmission. The impedance of a string is given by the ratio of its tension to the mass per unit length. The behavior of the wave at the boundary between the two strings can be analyzed using the wave equations and boundary conditions.

(i) Equations of Particle Displacement

Let’s denote the displacement of the wave on the first string (before the boundary) by y1(x,t)y_1(x, t) and on the second string (after the boundary) by y2(x,t)y_2(x, t).

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