A transverse periodic wave is represented by the equation y(x, t) = A1 sin(ωt − kx). Another transverse wave is represented by the equation y(x, t) = A2 sin(ωt + kx). What is the equation that represents the superposition of the two waves?
A) y(x, t) = (A1 + A2) sin(ωt) cos(kx) + (+A1 + A2) cos(ωt) sin(kx)
B) y(x, t) = (A1 + A2) sin(ωt) cos(kx) + (−A1 − A2) cos(ωt) sin(kx)
C) y(x, t) = (A1 − A2) sin(ωt) cos(kx) + (−A1 + A2) cos(ωt) sin(kx)
D) y(x, t) = (A1 + A2) sin(ωt) cos(kx) + (−A1 + A2) cos(ωt) sin(kx)

Question

Quizplus · Accepted Answer

When two waves with the same frequency and amplitude travelling in opposite directions are superimposed, the resulting wave is given by: y(x, t) = A1 sin(ωt − kx) + A2 sin(ωt + kx)
y(x, t) = A1 sin(ωt) cos(kx) − A1 cos(ωt) sin(kx) + A2 sin(ωt) cos(kx) + A2 cos(ωt) sin(kx)
y(x, t) = (A1 + A2) sin(ωt) cos(kx) + (-A1 + A2) cos(ωt) sin(kx)
Thus, the correct option is D.

A Transverse Periodic Wave Is Represented by the Equation Y(x