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

Question

Quizplus · Accepted Answer

The equation for the superposition of waves is given by:
y(x,t) = y1(x,t) + y2(x,t) = A1 sin(kx- ωt) + A2 sin(kx+ ωt)
Rewriting this in terms of trigonometric functions, we get:
y(x,t) = (A1 + A2) cos(ωt) sin(kx) + (A1 - A2) sin(ωt) cos(kx)
Comparing this with the given options, we see that the correct answer is D.

A Transverse Periodic Wave Is Represented by the Equation Y(x,t) ω\omegaω

A Transverse Periodic Wave Is Represented by the Equation Y(x,t) $\omega$