JEE Main · PhysicsHard

$A wave pulse travels on a string with tension T and mass per unit length μ . The string is joined to another string of mass per unit length 4 μ . What is the ratio of the amplitude of the reflected wave to the incident wave?$

Show correct answer & step-by-step solution

Correct answer: B — $- 1/3$

Solution

$The wave speeds are v_{1} = T / μ and v_{2} = T /4 μ = v_{1} /2 .$
$The reflection coefficient R is given by R = \frac{v _{2} - v _{1}}{v _{2} + v _{1}} .$
$Substituting the values, R = \frac{v _{1} /2 - v _{1}}{v _{1} /2 + v _{1}} .$
$This simplifies to R = \frac{- v _{1} /2}{3 v _{1} /2} = - 1/3 .$
$Hence the answer is (B).$