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A wave represented by the equation y=acos(kx-ωt) is superposed with another wave to form a stationary wave such that point x=0 is a node. The equation for the other wave is?

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A wave represented by the equation y=acos(kx-ωt) is superposed with another wave to form a stationary wave such that point x=0 is a node. The equation for the other wave is?

(a) acos(kx-ωt)

(b) -acos(kx-ωt)

(c) -acos(kx+ωt)

(d) -asin(kx-ωt)

This question was addressed to me in an online quiz.

The origin of the question is Transverse Waves topic in section Waves of Engineering Physics I

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Correct option is (c) -acos(kx+ωt)

Explanation: For the formation of a stationary wave, two identical waves travelling in opposite directions must separate each other. At x=0, resultant y should be zero for getting a node. Hence -acos(kx+ωt) is the correct answer.

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