Finding the slop of a string (Waves)

[cse63146]

Homework Statement

Wave motion is characterized by two velocities: the velocity with which the wave moves in the medium (e.g., air or a string) and the velocity of the medium (the air or the string itself).

Consider a transverse wave traveling in a string. The mathematical form of the wave is

$$y(x,t) = Asin(kx - \omega t)$$

Find the slope of the string $$\frac{dy(x,t)}{dx}$$ as a function of position x and time t.

Homework Equations

The Attempt at a Solution

So to find the slope of that equation, I would just need to take it's derivative. x is the variables, and $$\omega$$, A, t are constants. I would also need to use the chain rule when doing the derivative of sin.

So I get: $$\frac{dy(x,t)}{dx} = (Acos(kx - \omega t))*(k - \omega t)$$

but it says I'm wrong. Any suggestions where I went wrong?

 

[robphy]

Check your result for consistency of units.

 

[Integral]

$$\frac d {dx} ( kx- \omega t)$$ = ?

 

[cse63146]

$$\frac d {dx} ( kx- \omega t)$$ = ?

would I treat the x as a variable and t as a constant?