Question

A standing wave is represented by y = 2A sin kx cos ωt. If one of the component waves is y₁ = Asin (ωt – kx). What is the equation of the second component wave?

Answer 1

As 2sin A cos B = sin(A + B) + sin(A – B)

∴  y = 2Asin kx cos ωt

= Asin(kx + ωt) + Asin(kx − ωt)

According to superposition principle,

y = y₁ + y_2, 

And  y₁= A sin (ωt – kx)

= −A sin (kx – ωt)

y₂ = y − y₁ = 2Asin kx cos ωt  + Asin(kx − ωt)

= Asin(kx − ωt) + 2Asin(kx − ωt)

= Asin(kx − ωt) − 2Asin(kx − ωt)