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Question

The stationary wave y=2a sinkx cosωt in a stretched string is the result superposition of y1=asin(kxωt) and

A
y2=acos(kx+ωt)
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B
y2=asin(kx+ωt)
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C
y2=acos(kxωt)
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D
y2=asin(kxωt)
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Solution

The correct option is B y2=asin(kx+ωt)
y1=asin(kxωt)
y2=asin(kx+ωt)
According to the principle of superposition, the resultant wave is
y=y1+y2=asin(kxωt)
Using trigonomatric identity
sin(A+B)+sin(AB)=2sinAcosB
we get, y=2asin(kx)×cos(ωt)

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