A wave represented by `y=100sin(ax+bt)` is reflected from a dense plane at the origin.If `36%` of energy is lost and rest of the energy is reflected then the equation of the reflected wave will be -

Options

A. `y=-8.1sin(ax-bt)`
B. `y=8.1sin(ax+bt)`
C. `y=-80sin(ax-bt)`
D. `y=-10sin(ax-bt)`

Answer

A

Explanation

`I_(r )=I_(i)-(36)/(100)I_(i)=(64)/(100)I_(i)`
As `A prop sqrt(I)implies(A_(r ))/(A_(i))=sqrt((I_(r ))/(I_(i)))=sqrt((64)/(100))=(8)/(10)`
`impliesA_(r )=(8)/(10)A_(i)=(8)/(10)xx100=80` units
Due to reflection at rigid end, an additional phase II is created `:.y_(r )=A_(r )sin(ax-bt+pi)`