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Question
Equation of a plane progressive wave is given by `y = 0.6 sin 2π (t - x/2)`. On reflection from a denser medium its amplitude becomes 2/3 of the amplitude of the incident wave. The equation of the reflected wave is ______.
Options
`y = 0.6 sin 2π (t + x/2)`
`y = - 0.4 sin 2π (t + x/2)`
`y = 0.4 sin 2π (t + x/2)`
`y = - 0.4 sin 2π (t - x/2)`
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Solution
Equation of a plane progressive wave is given by `y = 0.6 sin 2π (t - x/2)`. On reflection from a denser medium its amplitude becomes 2/3 of the amplitude of the incident wave. The equation of the reflected wave is `underline(y = - 0.4 sin 2π (t + x/2))`.
Explanation:
The amplitude of a reflected wave `A_r = 2/3 xx A_i = 2/3 xx 0.6` = 0.4 units
Given the equation of incident wave `y_i = 0.6 sin 2π (t - x/2)`
The Equation of reflected wave is `y_i = A_r sin 2π (t + x/2 + π)` ......[∵ At denser medium, phase changes by π]
The positive sign is due to the reversal of direction of the proportion
So, `y_r = - 0.4 sin 2π (t + x/2)` ......[∵ sin(π + θ) = – sinθ]
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