1.

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»

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 + y2, 

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)



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