ye(x) is an envelop it depends only on the positions and yt(t) it depends only on the time. Using the equation1 y(x,t)=A sin(kxâ’ωt) we can find ye(x) and yt(t). Here x value is positive so we can alter that equation1 in positively that is equation2 y(x,t)=Asin(kx+ωt). Let y(x,t)=A sin(kxâ’ωt)=A (sin(kx)cos(ωt)â’cos(kx)sin(ωt)).
Sum of equation1 and equation2 then the result is 2A sin(kx),sin(ωt).
