A travelling wave $\mathrm{y} = \mathrm{A} \sin (\mathrm{kx}-\mathrm{\omega t}+\mathrm{\theta })$ 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:

• A

  ${\mathrm{y}}^{\text{'}} = 0.5\mathrm{Asin}(\mathrm{kx}+\mathrm{\omega t}+\mathrm{\theta })$

• B

  ${\mathrm{y}}^{\text{'}} = -0.5\mathrm{Asin}(\mathrm{kx}+\mathrm{\omega t}+\mathrm{\theta })$

• C

  ${\mathrm{y}}^{\text{'}} = -0.5\mathrm{Asin}(\mathrm{\omega t}-\mathrm{kx}-\mathrm{\theta })$

• D

  ${\mathrm{y}}^{\text{'}} = -0.5\mathrm{Asin}(\mathrm{kx}+\mathrm{\omega t}-\mathrm{\theta })$