At time t = 0, the shape of a pulse on a very long string is described by y(x,0) = f(x). The pulse subsequently travels without distortion towards the positive x-direction with constant speed v. Which expression gives the displacement at a later time t?
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Question

At time t = 0, the shape of a pulse on a very long string is described by y(x,0) = f(x). The pulse subsequently travels without distortion towards the positive x-direction with constant speed v. Which expression gives the displacement at a later time t?

Options

G1 Physics · Accepted Answer

For a pulse moving to the right with speed v, the same phase point that was at x₀ at t = 0 will be at x = x₀+vt. Therefore, x₀ = x−vt. The entire initial profile must therefore be evaluated at x−vt. Hence, y(x,t) = f(x−vt). Correct option: A.