A travelling wave $y = A \sin (kx - ωt + θ)$ passes from a heavier string to a lighter string. The reflected wave has amplitude 0.5 A. The junction of the strings is at x = 0. The equation of the reflected wave is:

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$y^{'} = - 0.5 Asin (kx + ωt + θ)$

$y^{'} = - 0.5 Asin (ωt - kx - θ)$

$y^{'} = 0.5 Asin (kx + ωt + θ)$

$y^{'} = - 0.5 Asin (kx + ωt - θ)$

answer is D.

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Detailed Solution

As wave has been reflected from a rarer medium, therefore there is no change in phase. Hence equation for the opposite direction can be written as

$y = 0.5 Asin (- kx - ωt + θ)$

= -0.5 $Asin (kx + ωt - θ)$

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