(a) Plot the time-independent wave function for the traveling pulse described by the time-dependent wave function

\[D_{y}(x, t)=\frac{a}{b^{2}+(x-a)^{2}}\]

with \(a=5.0 \mathrm{~m}^{3}, b=1.0 \mathrm{~m}\), and \(c=2.0 \mathrm{~m} / \mathrm{s}\) for \(t=0\), \(1.0 \mathrm{~s}, 2. 0 \mathrm{~s}\), and \(3.0 \mathrm{~s}\).

(b) What is the wave speed \(c\) of this pulse?