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## Homework Statement

Consider a string of infinite extent made up of two homogeneous strings of different densities joined at x=0

In each region u

_{tt}-c

^{2}

_{j}u

_{xx}=0

j=1,2

c

_{1}≠c

_{2}

we require continuity of u and u

_{x}at x=0

suppose at t<0 a wave approaches x=0 from the left.

IE: as t approaches 0 from the negative values

u(x,t) = F(x-c

_{1}t) when x<0 t[itex]\leq[/itex]0

and = 0 when x>0 t[itex]\leq[/itex]0

as t increases further, the wave reaches x=0 and gives rise to reflected and transmitted waves.

(a) formulate the appropriate initial values for u at t=0

(b) solve the initial value problem for -∞<0<∞ t>0

(c) identify the incident, reflected, and transmitted waves in your solution and determine the reflection and transmission coefficients for the junction in terms of c

_{1}and c

_{2}. Comment on your values in the limit c

_{1}[itex]\rightarrow[/itex]c

_{2}

## Homework Equations

My textbook has a small section on infinite strings but nothing about different densities.

I also need examples in order to understand the theory.

There are no examples :(

## The Attempt at a Solution

No attempt.

I need help frm the bottom up.

I need examples.

I cannot understand by just looking at the theory.

If someone can please HELP.

thanks so much guys

you're my heroes.