A composite string is made up by joining two strings of different masses per unit length rightarrow `mu and 4mu` the composite string is under the same tension A transverse wave pulse Y=(6mm) sin (5t+40x) where is in seconds and x in metres is sent along the lighter string towards the joint the joint is at x=0 the equation of the wave pulse reflected from the joint is

Options

A. `(2mm)sin (5t_40x)`
B. `(4mm)sin (40x-5t)`
C. `-(2mm)sin (5t-40x)`
D. `(2mm)sin(5r-10x)`

Answer

C

Explanation

`V_(1)=sqrt(T/mu) , V_(2)=sqrt(T/(4mu))V_(2)leV_(1)`
`Rightarrow2^(nd) is danser Rightarrow phase change of pi`
wave reflected from denser medium
`Rightarrow A_(r)=(V_(2)_V_(1))/V_(2)+V_(1)xx6=(v_(1)/2-V_(1))/(V_(2)/2+V_(1))xx6=-2mm`
`eq^(n) Rightarrow -(2mm)sin (5t-40x)`