Understanding the Standing Wave Equation: A Guide for Students

[Voidy]

Homework Statement

Homework Equations

y (x,y) = 2YmSin(kx)Cos(wt)

The Attempt at a Solution

I am having trouble at setting up the standing wave equation for this problem.

Once I set up the equation, I know that part a b c d is just plugging in the numbers.

From what I learned, I know that the standing wave equation is

Y(x,y) = 2YmSin(kx)Cos(wt), this is what the textbook states.

(Ym being the amplitude).

I calculated k and w correctly.

The equation I set up was Y(x,y) = .041Sin(kx)Cos(wt)

However, the solution uses the equation

Y(x,y) = -2YmCos(kx)Sin(wt).

therefore,

Y(x,y) = -.041Cos(kx)Sin(wt)

I do not understand why there is a negative sign in front of the amplitude and why Sin and Cos is switched in the equation used by the solution.

Any help or guide will be greatly appreciated, Thank you.

 

[RUber]

The form used in the solution is based off the plot. The plot at x = 0, with t varying implies that the kx term has to be inside a cosine function--otherwise your plot at x = 0 would be a flat line. The plot shows at t=0, y=0, so the wt term should be inside a sine function. Finally, the y value first dives into negative territory, as t is small and positive, so you would want a negative sine of wt function in order to do that.