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Mechanical Properties Of Fluids

Question
CBSEENPH11018950

Waves of intensity level 27.96db and 30.88db from two coherent sources interfere. A detector is moved along the line perpendicular to right bisector of two sources. Find the intensity at the point where constructive and destructive inference takes place. Take antilog 2.796 = 625, antilog 3.088 = 1225 and threshold of hearing 1pW/m2.

Solution
The intensity of wave from the first source is, 
straight I subscript 1 space equals space straight I subscript straight o space Antilog space open parentheses straight L subscript 1 over 10 close parentheses space

space space space equals space straight I subscript straight o space Antilog space open parentheses fraction numerator 27.96 over denominator 10 end fraction close parentheses

space space space equals space 625 space straight I subscript straight o space

The space intensity space of space wave space from space second space source space is comma space

straight I subscript 2 space equals space straight I subscript straight o space Antilog space open parentheses straight L subscript 2 over 10 close parentheses space

space space space space equals space straight I subscript straight o space Antilog space open parentheses fraction numerator 30.88 over denominator 10 end fraction close parentheses space

space space space space space equals space 1225 space straight I subscript straight o space

At space constructive space interference comma space

straight I subscript max space equals open parentheses square root of straight I subscript 2 end root space plus space square root of straight I subscript 1 end root close parentheses squared space

space space space space space space space space space equals space open parentheses square root of 1225 space straight I subscript straight o end root space plus space square root of 625 space straight I subscript straight o end root close parentheses squared space

space space space space space space space space space equals space 60 space straight I subscript straight o space equals space 60 space cross times space 10 to the power of negative 12 end exponent space straight W divided by straight m squared space

At space destructive space interference comma space

straight I subscript min space equals open parentheses square root of straight I subscript 2 end root space minus space square root of straight I subscript 1 end root close parentheses squared space space

space space space space space space equals space open parentheses square root of 1225 space straight I subscript straight o end root space minus space square root of 625 space straight I subscript straight o end root close parentheses squared space

space space space space space space equals space 10 space straight I subscript straight o space equals space 10 space cross times space 10 to the power of negative 12 end exponent space straight W divided by straight m squared