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## Homework Statement

Given that a string is constrained such that dy/dx = 0 at x = 0 and unconstrained otherwise, what is the reflected and transmitted power?

y is the deflection of the string from the x-axis. y_1 is incident wave, y_r is reflected and y_t is transmitted.

## Homework Equations

Reflected power, transmitted power have already been derived in terms of impedances.

[tex] Impedance Z = \frac{Driving Force}{string element velocity} [/tex]

Continuity of y and dy/dx.

## The Attempt at a Solution

Knowing that y and dy/dx are continuous, I wrote [itex] \frac{\partial y_1}{\partial x} +\frac{\partial y_r}{\partial x} = \frac{\partial y_t}{\partial x} =0 [/itex] at x = 0.

Substituting in the general solution [itex] y_1 = e^{-ikx+iwt}, y_r = re^{+ikx+iwt}, y_t = te^{-ikx+iwt} [/itex];

I got 1 + r = t and 1 - r = t = 0 at x = 0.

The latter suggests all reflection, no transmission, which isn't correct because it doesn't satisfy the first equation.

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