Q. Two strings with mass per unit length of 9 $gcm^{- 1}$ and $25\ gcm^{- 1}$ are joined together in series. The reflection coefficient for the vibration waves are

A) $\frac{9}{25}$
B) $\frac{3}{5}$
C) $\frac{1}{16}$
D) $\frac{9}{16}$
Explanation

(c) Let $I_{r}and\ I_{i}$ represent the intensities of reflected and incident waves respectively, then
$\frac{I_{r}}{I_{i}} = \left( \frac{\mu - 1}{\mu + 1} \right)^{2}$
$Where\ \mu = \frac{v_{1}}{v_{2}}$
$Or\ \ \ \ v = \frac{\sqrt{\frac{T}{m_{1}}}}{\sqrt{\frac{T}{m_{2}}}} = \sqrt{\frac{m_{2}}{m_{1}}} = \sqrt{\frac{25}{9}} = \frac{5}{3}$
$\therefore\frac{I_{r}}{I_{i}} = \left\lbrack \frac{\left( \frac{5}{3} \right) - 1}{\left( \frac{5}{3} \right) + 1} \right\rbrack^{2} = \frac{1}{16}$

Dr. Abubacker
Reviewed by Dr. Abubacker

Physics Educator & NEET/JEE Specialist

Ph.D. in Physics with 19+ years of teaching experience.

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