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Find the damping coefficient v of a sound wave if at distances `r_(1)=10m` and `r_(2)=20 m` from a point isotropic source of sound the sound wave intensity values differ by a factor `eta=4.5`. |
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Answer» Intensity of a spherical sound wave emitted from a point source in a homogeneous absorbing medium of wave damping coefficient `gamma` is given by `I=(1)/(2) rho a^(2) e^(-2gammar)omega^(2) v` So, Intensity of sound at a distance `r_(1)` from the source `(I_(1))/(r_(1)^(2))=(1//2rho a^(2) e^(-2gamma r_(1))omega^(2) v)/(r_(1)^(2))` and intensity of sound at a distance `r_(2)` from the source `=I_(2)//r_(2)^(2)=(1//2rhoa^(2)e^(-2gammar_(2))omega^(2)v)/(r_(2)^(2))` But according to the problem `(1)/(eta)(I_(1))/(r_(1)^(2))=(I_(2))/(r_(2)^(2))` So, `(etar_(1)^(2))/( r_(2)^(2))=e^(2 gamma(r_(2)-r_(1)))`or`1n(etar_(2)^(2))/(r_(1)^(2))=2 gamma(r_(2)-r_(1))` or,` gamma =(1n(etar_(2)^(2)//r_(1)^(2)))/(2(r_(2)-r_(1)))=6xx10^(-3)m^(-1)` |
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