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Question

A wave represented by the equation Y=Acos(kxωt) is superimposed with another wave to form a stations wave such that the point x=0 is a node. The equation of the other wave is

A
Asin(kx+ωt)
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B
Acos(kx+ωt)
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C
Asin(kx+ωt)
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D
Acos(kx+ωt)
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Solution

The correct option is C Acos(kx+ωt)
Given wave is : Acos(kxωt)=A[coskxcosωt+sinkxsinωt]
Since we need node at x=0, we need to cancel coskx term in the sum of given wave and superimposed wave
Hence superimposed wave is of the form

(Acoskxcosωωt+Asinkxsinωt)=A[coskxcosωtsinkxsinωt]=Acos(kx+ωt)

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