- #1

Adrian Simons

- 10

- 4

- Homework Statement
- This is Problem #71 in Chapter 15 of Paul A. Tipler and Gene Mosca, PHYSICS For Scientists and Engineers, Sixth Edition,

W. H. Freeman & Co., New York, NY, 2008.

- Relevant Equations
- $$1 = r^2 + \left( \frac{v_1}{v_2} \right) \tau^2$$ where ##\tau## and ##r## are the transmission and reflection coefficients given by $$\tau = \frac{2 v_2}{v_2 + v_1}$$ and $$r = \frac{v_2 - v_1}{v_2 + v_1}$$.

The statement of the problem is:

Consider a taut string that has a mass per unit length ##\mu_1## carrying transverse wave pulses of the form ##y = f(x - v_1 t)## that are incident upon a point P where the string connects to a second string with mass per unit length ##\mu_2##.

Derive $$1 = r^2 + \left( \frac{v_1}{v_2} \right) \tau^2$$ by equating the power incident on point P to the power reflected at P plus the power transmitted at P.

The solution given in the solutions manual to the textbook is wrong. There is one glaring error in it, in addition to what I believe are some more subtle errors. Also, there are several things they do without any motivation for why they're doing it, which I believe are incorrect. Otherwise, I've been unable to solve the problem. Can anyone provide a viable solution?

Consider a taut string that has a mass per unit length ##\mu_1## carrying transverse wave pulses of the form ##y = f(x - v_1 t)## that are incident upon a point P where the string connects to a second string with mass per unit length ##\mu_2##.

Derive $$1 = r^2 + \left( \frac{v_1}{v_2} \right) \tau^2$$ by equating the power incident on point P to the power reflected at P plus the power transmitted at P.

The solution given in the solutions manual to the textbook is wrong. There is one glaring error in it, in addition to what I believe are some more subtle errors. Also, there are several things they do without any motivation for why they're doing it, which I believe are incorrect. Otherwise, I've been unable to solve the problem. Can anyone provide a viable solution?

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