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Corresponding to displacement equation, ...

Corresponding to displacement equation,
`y =A sin (kx+omegat)`
of a longitudinal wave make its pressure and density wave also. Bulk modulus of the medium is `B` and density is `p`.

Text Solution

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The correct Answer is:
A, B, C, D
Give, `y (x, t) = A sin (kx + omegat)`
`(dely)/(delx) =kA cos (kx + omegat)` ..(i)
Now, pressure equation is given by
`Deltap = - B((dely)/(delx))`
subsituting the value of `(dely)/(delx)` from Eq. (i) we have
`Deltap = - BAk cos (kx+ omegat)`
Similarly, density equation is give by
`(Delta p) = (rho)/(B) (Deltap) = (rho)/(B) (-B(dely)/(delx)) = - rho ((dely)/(del x))`
substituting the value of `(dely)/(delx)` from Eq. (i), we have,
`Delta rho = - rho Ak cos (kx + omegat)`
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