When two waves of amplitudes 3 unit and 5 unit superpose at some point, find ratio of maximum to minimum intensity.

Options

A. `2:1`
B. `5:3`
C. `4:1`
D. `16:1`

Answer

D

Explanation

We know that `I= prop a ^(2)`
`therefore I _(max) prop a _(max) ^(2)`
`therefore I _(max) prop (a _(1) + a _(2)) ^(2) " "...(1)`
Similarly `I_(min)prop a _(min) ^(2) `
`therefore I _(min ) prop (a _(1) -a _(2)) ^(2) " "...(2)`
From (1) and (2),
`(I _(max ))/( I _(min )) = ((a _(1) + a _(2) ) ^(2))/( (a _(1) -a _(2)) ^(2))`
`therefore (I _(max))/( I _(min )) = ((3 + 5 ) ^(2))/( (3 -5) ^(2)) = (64)/(4) = (16)/(1) = 16:1`