Transverse Wave Pulse

Squires

A transvers wave pulse travels to the right (+x direction) along a string with a speed v=3m/s. At t=0, the shape of the pulse has the form:

f(x)=Ae^-(x^2/b^2), where A=3m and b=2m.

a) Plot the variation of f(x) with x at t=0.
b) What will the mathematical description of the pulse as a function of time, f(x,t), assuming that the pulse moves without changing its shape.
c)Sketch the profile of the wave pulse at t=2s.


I'm guessing the position with time is dependant on the velocity, but I'm totally confused at what the variation will even look like, as i've never come across an exponential to x^2 function before.

Thanks for looking.