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Question

A wave represented by the equation y=Asin(kxωt) is superimposed with another wave to form a stationary 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(kxωt)
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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 B Acos(kxωt)
The given wave has the wave function,
y=Acos(kx+ωt)
Let, the other wave has the wave function y.
At node i.e. stationary point, x=0 and the sum of individual wave functions, y and y must be zero at x=0 at all times.
Therefore,
y(0,t)=y+y=0
y=y
Therefore,
y=Acos(kx+ωt)
The first (-) shows that the second wave is like an inverted wave with respect to the first wave. This is the required equation of the other wave.

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