Distortion of Gaussian pulse

1. The problem statement, all variables and given/known data
In a string with both ends fixed, a gaussian pulse in the form ψ=Ae-aw2 where w=z-vt and v is its velocity is propagating. We are asked to find:
a) The transverse velocity for every following moment.
b) The maximum transverse velocity.
c) To check if there is distortion in the shape of the string as it propagates.

2. Relevant equations

3. The attempt at a solution
I’ve solved a and b but i have no idea how to check for the distortion. I think this depends on the string and our approximation as to if it is continuous or not.

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