The stationary wave y=2asinkxcosωt in a stretched string is the result superposition of y1=asin(kx−ωt) and
A
y2=acos(kx+ωt)
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B
y2=asin(kx+ωt)
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C
y2=acos(kx−ωt)
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D
y2=asin(kx−ωt)
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Solution
The correct option is By2=asin(kx+ωt) y1=asin(kx−ωt) y2=asin(kx+ωt) According to the principle of superposition, the resultant wave is y=y1+y2=asin(kx−ωt) Using trigonomatric identity sin(A+B)+sin(A−B)=2sinAcosB we get, y=2asin(kx)×cos(ωt)