What is the wave speed and string velocity for y(x,t) = 3e^-(2x-4t)^2?

[Faux Carnival]

Homework Statement

y(x,t) = 3e^{-(2x-4t)^2}

Consider the wave function which represents a transverse pulse that travels on a string along the horizontal x-axis.

a) Find the wave speed
b) Find the velocity of the string at x=0 as a function of time

Homework Equations

The Attempt at a Solution

I think, for b) I should take the derivative of the original wave function with respect to t.
Easy if that's the case.

I have no idea about part a.

 

[merryjman]

http://en.wikipedia.org/wiki/Wave_equation

http://mathworld.wolfram.com/WaveEquation.html

Looking at these pages, you can see that the second partial derivative of the wave function with respect to time is equal to the square of the speed multiplied by the second partial derivative of the wave function with respect to position.

 

[Faux Carnival]

Wow, thanks merry. I completely forgot about the linear wave equation.

And is my solution for part b correct? (Taking the derivative of the function with respect to time to find the string velocity function)

 

[merryjman]

I would say so. At x = 0 that wave function gives Y position as a function of time, so its time derivative would be the rate of change of the Y position.