In a stationary wave pattern that forms as a result of reflection pf waves from an obstacle the ratio of the amplitude at an antinode and a node is `beta = 1.5.` What percentage of the energy passes across the obstacle ?

Explanation

We know that,
`(A_(max))/(A_("min"))=(A_(i)+A_(r))/(A_(i)-A_(r))=(3)/(2)` (given)
`2A_(i)+2A_(r)=3A_(i)-3A_(r)`
`2A_(r)+3A_(r)=3A_(i)-2A_(i)`
`5A_(r)=A_(i)`
`(A_(r))/(A_(i))=(1)/(5)`
`(l_(r))/(l_(i))=((A_(r))/(A_(i)))^(2)=((1)/(5))^(2)=(1)/(25)`
`l_(r)=0.04l_(i)`
`because4%` of the incidennt energy is reflected or 96% energy passes across the obstacle.