The equation for spherical progressive wave is (where $r$ is the distance from the source)
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(d) For spherical wave intensity $(I) \propto \frac{1}{{{{({\rm{Distance}}\,r)}^2}}}$
also $I \propto {a^2}$ ==> $a \propto \frac{1}{r}$. Hence equation of a cylindrical wave is $y = \frac{1}{r}\sin (\omega t - kx)$
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