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A wave travelling along positive x-axis is given by y = A sin( $ω$ t–kx). If it is reflected from a rigid boundary such that 80% of its amplitude is reflected, then the equation of reflected wave is

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y = -0.8A sin( $ω$ t + kx)

y = A sin( $ω$ t + kx)

y = 0.8A sin( $ω$ t + kx)

y = A sin( $ω$ t + 0.8kx)

answer is B.

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Detailed Solution

y_i = a_i sin(wt - kx) = A sin(wt - kx)
In reflected wave a phase difference of $π$
y_r = a_r sin(wt - kx + $π$ ) = 80%Asin(wt + kx)
y_r = 80% A sin( $ω$ t + kx + $π$ )
y_r = -0.8A sin( $ω$ t + kx)

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