Question

A wave travels on a light string. The equation of the wave is $y=Asin(kx+wt+{30}^{\circ }+{180}^{\circ })$, it is reflected from a heavy string tied to an end of the light string at x= 0. If 64% of the incident energy is reflected then what is the equation of the reflected wave?

• A. $y=Asin(kx-wt+{30}^{\circ })$
• B. $y=Asin(kx+wt+{30}^{\circ })$
• C. $y=0.8Asin(kx-wt+{30}^{\circ })$
• D. $y=0.8Asin(kx+wt+{30}^{\circ })$

Answer 1

The correct option is C $y=0.8Asin(kx-wt+{30}^{\circ })$

Energy reflected = 64% of incident energy
Hence, amplitude of reflected wave $=\sqrt{\frac{64}{100}}A=0.8A$
As wave is reflected from a denser medium, phase change of ${180}^{\circ }$ will take place. Moreover, it will travel along negative x-axis.
Hence, equation of reflected wave is $y=0.8Asin(kx-wt+{30}^{\circ })$