Drawing a contour map for e^(variable)sine(x-t*variable)

[mrcleanhands]

Homework Statement

Draw a contour map for $T(x,t)=10e^{-\lambda x}\sin(\omega t-\lambda x)$

$0\leq\lambda x\leq2\Pi$ and $0\leq\omega t\leq2\Pi$

Homework Equations

The Attempt at a Solution

Because those two variables are within that given range I'm not sure how to do this.

Normally I would set f(x,y) to k and then see if a function could be drawn on the x-y plane for any given value of k. so you might get a circle of radius k. but here I'm thrown off.

sin varies between -1 and 1 and $10e^{-\lambda x}$ between 10 an $10e^{-2\Pi}$

 

[mighty2000]

so I think I need to graph it on the Z axis.


I suggest using a computer program or graphing calculator to plot the contour map for T(x,t). This will give you a visual representation of the function and help you understand how it changes with different values of x and t.

To create a contour map, you will need to plot points on a grid with x and t as the two axes. Then, for each point on the grid, calculate the value of T(x,t) using the given equation. The resulting values can then be plotted on a third axis, representing the value of T(x,t).

Alternatively, you can plot the function as a surface plot, where the x and t axes represent the independent variables and the height of the surface represents the value of T(x,t). This will give you a three-dimensional representation of the contour map.

I also suggest experimenting with different values of λ and ω to see how they affect the contour map. This will give you a better understanding of the relationship between these variables and the resulting contour map.

Overall, creating a contour map for T(x,t) will help you visualize the function and better understand its behavior. This can be a useful tool for analyzing and interpreting data in your scientific research.