At t = 0, a localized pulse on a string has the shape y(x,0) = A/[1+(x/a)²]. It propagates towards the negative x-direction with speed v without changing shape. Which expression correctly represents the pulse at time t?
Options

Question

At t = 0, a localized pulse on a string has the shape y(x,0) = A/[1+(x/a)²]. It propagates towards the negative x-direction with speed v without changing shape. Which expression correctly represents the pulse at time t?

Options

G1 Physics · Accepted Answer

A wave moving towards −x has the general form y = f(x+vt). The initial profile is f(x) = A/[1+(x/a)²]. Therefore, y(x,t) = A/{1+[(x+vt)/a]²}. Correct option: B.