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?

Two sound waves from two different sources interfere at a point to yie

1.	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?
Answer» 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)`

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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?

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