# Wave function for transverse waves on a rope

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1. May 31, 2015

### arestes

1. The problem statement, all variables and given/known data
Serway's Physics for Sciencetists and Engineers with Modern Physics, 9th Edition (current), Chapter 16, problem 19:

(a) Write the expression for y as a function of x and t in SI units for a sinusoidal wave traveling along a rope
in the negative x direction with the following characteristics:
A = 8.00 cm, $\lambda$= 80.0 cm, f = 3.00 Hz, and y(0, t) = 0 at t = 0. (b) What If? Write the expression for y as a function of x and t for the wave in part (a) assuming y(x, 0) = 0 at the point x = 10.0 cm.

2. Relevant equations
$$y(x,t)=ASin\left(kx\pm \omega t +\phi \right) \\k=\frac{2\pi}{\lambda} \\\omega=2\pi f$$
And the fact that the minus sign inside the Sine corresponds to a wave traveling along the +x direction and the plus sign to the -x direction.
3. The attempt at a solution
k and $\omega$ are readily given by the formulas above. The direction of the wave chooses the right sign inside the Sine. Only problem is the initial phase $\phi$. Using the given data: at t=x=0 we must have:
$$Sin(\phi)=0$$ which, by trigonometry, corresponds to TWO solutions ( modulo 2 pi): Either $\phi=0$ or $\phi=\pi$ BUTthe solutions at the end of the book (odd numbered problems, Serway's Physics for Scientists and Engineers with Modern Physics, 9th Edition (current), Chapter 16, problem 19, page 502, whose solution is given on page A-38 at the end of the book), gives only the first solution and says nothing about the second (with initial phase being pi).
Part (b) is just the same.

This cannot be discarded, I think. It fulfills all the given conditions, right? Am I missing something here? Does the direction of propagation of the wave influence on picking out only one of the two?
thanks

2. May 31, 2015

### haruspex

I agree with you.

3. May 31, 2015

### arestes

thanks. But i'm surprisedd serway wouldn's say anything about the other solution. This problem's been there since at least the seventh edition