The equation of a wave is $\mathrm{Y}=\mathrm{A} \sin (2 \pi \mathrm{vt}) / \lambda$ When it is refl

Question

The equation of a wave is $\mathrm{Y}=\mathrm{A} \sin (2 \pi \mathrm{vt}) / \lambda$ When it is reflected at a rigid support, its amplitude becomes $90 \%$. The equation of the reflected wave is\

Professor PC Thomas Classes · Answer

When a wave gets reflected at a rigid boundary it gets inverted. The inversion is indicated by a -ve sign. If $90 \%$ of the wave is reflected $A$ becomes 0.9 A . Thus the equation of incident wave is $y=A \sin \frac{2 \pi v t}{\lambda}$. The equation of reflected wave is $\mathrm{y}^{\prime}=-0.9 \mathrm{~A} \sin \frac{2 \pi \mathrm{vt}}{\lambda}$. But this answer is not there. Use the equation $-\sin 	heta=\sin (	heta+\pi)$.\ Then $\mathrm{y}^{\prime}=0.9 \mathrm{~A} \sin \left(\frac{2 \pi \mathrm{vt}}{\lambda}+\piight)$\