Answer to Question #54841 in Physics for MAYANK BISHT

Question

5. 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. (3+2+5)
b) Two waves, travelling along the same direction, are given by
( , ) sin( ) 1 1 1
y x t = a ω t − k x
and
( , ) sin( ) 2 2 2
y x t = a ω t − k x
Suppose that ω1
and 1
k are respectively slightly greater than ω2
and . 2
k i) Obtain an
expression for the resultant wave arising due to their superposition and ii) explain the
formation of wave packets.