# Expression y(x,t) for sinusoidal wave traveling along a rope

1. May 14, 2016

### horsedeg

1. The problem statement, all variables and given/known data
(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 = 5.00 cm, λ =85.0 cm, f = 5.00 Hz, and y(0, t) = 0 at t = 0. (Use the following as necessary: x and t.)

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 = 17.0 cm. (Use the following as necessary: x and t.)
2. Relevant equations
Conversion equations from f and lambda to k and omega
y(x,t) = Asin(kx(+/-)wt)

3. The attempt at a solution
$$5\sin \left(10\pi t+\frac{2}{85}\pi x-.4\pi \right)$$
Why is this wrong? I don't understand. I put it into desmos, and it shows AT LEAST that at at y(17,0) = 0. Also based off the slider, it seems to be going in the negative x-direction, which is correct.

2. May 14, 2016

### robphy

SI units?

3. May 14, 2016

### horsedeg

So I'm supposed to put this in meters instead of centimeters?

I thought I tried that, but apparently I had other things wrong when I did. Thanks, I totally thought I had everything right.

4. May 14, 2016

### horsedeg

By the way, if you don't mind me asking, how are you supposed to tell whether or not a wave is going along the positive or negative x-direction? I know it has to do with the signs, but it would seem intuitive that the angular frequency being negative would mean it's negative. However, it appears that both k and omega being positive means that it's going in the negative x-direction. Why?

5. May 14, 2016

### robphy

Think "phase".
At an instant, consider a point on the string. Note its phase (the argument of the sin function).
As t increases, what must x do to keep this phase value (i.e. this disturbance) constant?
That's where the disturbance propagates to.

Old post:
https://www.physicsforums.com/threa...ean-in-the-wave-equation.836348/#post-5254546

https://www.desmos.com/calculator/bjt6dleg5h

6. May 14, 2016

### horsedeg

Simplified, does this mean that a minus means positive direction and a plus means negative direction?

7. May 14, 2016

### robphy

Relative-minus sign means the disturbance travels in the positive x-direction.