At \(t=0\), a wave pulse has a shape given by the timeindependent wave function

\[f(x)=\frac{a}{b^{2}+x^{2}}\]

where \(a=0.030 \mathrm{~m}^{3}\) and \(b=2.0 \mathrm{~m}\).

(a) If the pulse travels in the positive \(x\) direction at a wave speed of \(1.75 \mathrm{~m} / \mathrm{s}\), write the time-dependent wave function \(f(x, t)\) for this transverse wave.

(b) Plot the time-dependent wave function \(f(x, t)\) at \(t=-0.50 \mathrm{~s}\) and at \(t=+0.50 \mathrm{~s}\) over the range of \(x\) in which \(f(x, t)\) is substantially changing.

(c) Plot the displacement curve at \(x=2.0 \mathrm{~m}\).