Q. Two strings with masses per unit length of $25\ gcm^{- 1}$ and $9\ gcm^{- 1}$ are joined together in series. The reflection coefficient for the vibration waves is
A) $\frac{9}{25}$
B) $\frac{3}{5}$
C) $\frac{1}{16}$
D) $\frac{9}{16}$
Explanation
(c) Suppose $I_{i}\ and\ I_{r}$ are intensities of incident and reflected waves.
Reflection coefficient $= \frac{I_{r}}{I_{i}} = \left( \frac{\mu - 1}{\mu + 1} \right)^{2}$
Where $\mu = \frac{v_{1}}{v_{2}} = \frac{\sqrt{T/m_{1}}}{\sqrt{T/m_{2}}} = \sqrt{\frac{m_{2}}{m_{1}}} = \sqrt{\frac{25}{9}} = \frac{5}{3}$
$\therefore$ Reflection coefficient $= \left( \frac{5/3 - 1}{5/3 + 1} \right)^{2} = \frac{1}{16}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.