Chapter 15, Problem 94GP

(II) The displacement of a bell-shaped wave pulse is described by a relation that involves the exponential function:

$D\left(x,t\right)=A{e}^{-\alpha {\left(x-vt\right)}^2}$

where the constants A = 10.0 m, α = 2.0 m^–2, and v = 3.0 m/s. (a) Over the range –10.0 m ≤ x ≤ + 10.0 m, use a graphing calculator or computer program to plot D(x, t) at each of the three times t = 0, t = 1.0, and t = 2.0 s. Do these three plots demonstrate the wave-pulse shape shifting along the x axis by the expected amount over the span of each 1.0-s interval? (b) Repeal part (a) but assume $D\left(x,t\right)=A{e}^{-\alpha {\left(x+vt\right)}^2}$.