Two traveling waves, y₁ = A sin[k(x - vt)] and y₂ = A sin[k(x + vt)], are superposed on the same string.The distance between the adjacent nodes is: A)"vt/$\pi$" B)"vt/2$\pi$" C)"$\pi$/2k" D)"$\pi$/k" E)"2$\pi$/k"

Question

Quizplus · Accepted Answer

The superposition of the two waves results in a standing wave, described by y = 2A sin(kx) cos(kvt). The nodes occur where sin(kx) = 0, which is at kx = nπ, where n is an integer. The distance between adjacent nodes is given by Δx = π/k.

Two Traveling Waves, Y1 = a Sin[k(x - Vt)] and Y2

Two Traveling Waves, Y₁ = a Sin[k(x - Vt)] and Y₂