Two sound waves from two different sources interfere at a point to yield a sound of varying intensity. The intensity level between the maximum and minimum is 20 dB. What is the ratio of the intensities of the individual waves?

Explanation

If `I_(max)` and `I_(min)` are the maximum and minimum intensities of the resultant waves, then the intensity level between them will be
`L=10log((I_(max))/(I_(min)))dB`
or, `20dB=10log((I_(max))/(I_(min)))dB`
or, `(I_(max))/(I_(min))=(100)/(1)`
If `A_1` and `A_2` are the amplitudes of the individual waves, intereferring, then
`(I_(max))/(I_(min))=((A_1+A_2)^2)/((A_1-A_2)^2)`
`((A_1_A_2)/(A_1-A_2))^2=(100)/(1)`
`implies(A_1+A_2)/(A_1-A_2)=(10)/(1)`
or `(A_1)/(A_2)=(11)/(9)`
Therefore the intensity ratio between the individual waves will be
`(I_1)/(I_2)=((A_1)/(A_2))^2=(121)/(81)`