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

When two waves of amplitudes 3 unit and 5 unit superpose at some point

1.	When two waves of amplitudes 3 unit and 5 unit superpose at some point, find ratio of maximum to minimum intensity.
Answer» `2:1` `5:3` `4:1` `16:1` Solution :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`