Using trigonometric identities

Question

Use trigonometric identities to show for equations 1 and 2, their sum is given by equation 3

1. p1 = A sin (kx - ωt)

2. p2 = A sin (kx + ωt)

3. p = p1 + p2 = 2 A sin(kx) cos(ωt)

Answer 1

Hi

1. p1 = A sin (kx - ωt) = A [ sinkx coswt - coskx sinwt ]

2. p2 = A sin (kx + ωt)= A [ sinkx coswt + coskx sinwt ]

p = p1 + p2 = A [ sinkx coswt - coskx sinwt ] + A [ sinkx coswt + coskx sinwt ] after simplify you will have:

p = p1 + p2 = 2 A sin(kx) cos(ωt)

I hope it works for you,

Minoo

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