@wingho For me, also, the result seems somehat unintuitive, but I recall feeling this way at some point in my PDE's course some years ago as well...

As for the lack of response rounding, it's important to realize that the wave equation is an idealized model, and a practical model would need to take into account internal friction in the string, or any other potential cause of damping, which would manifest in the equations as a first order derivative term, sometimes as the square of the wave velocity (your zero 'd' coefficient in the original equation). In all likelihood, the higher frequencies will see more damping, which has the effect of rounding out the sharp edges.

Keeping a simple form for the friction (e.g. a linear velocity, d=1/10) would still allow one to proceed with separation of variables, but now the time equation would become 

tODE := diff(T(t), t, t)/T(t) + 1/10*diff(T(t), t)/T(t) = -(9*lambda^2)/4

The characteristing equation would have complex roots -1/20 +/- sqrt(-900*lambda^2 + 1)/20 which shows that the damping is uniform across all frequencies (exp-t/20), so in order to see the rounding, I suspect a square term is required, or a dependence of the damping on the velocity.