Density equation of sound wave

AI Thread Summary
The discussion focuses on deriving the density equation of a sound wave from the pressure equation given as ΔP = Po cos(ωt - kx). The user presents several equations, including the relationship between bulk modulus (B), pressure change (ΔP), and volume change (ΔV/V). The derivation leads to the expression for the change in density (∂ρ) in terms of the pressure and bulk modulus. The final equation presented is ∂ρ = (ρ Po/B) cos(ωt - kx), which seeks validation for its correctness. The conversation emphasizes the need for proof and proper explanation in the derivation process.
abhineetK
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Let pressure equation of sound wave be
\Deltap=Pocos(\omegat-kx), then
what will be the density equation of the sound wave?
give your answer with proof and proper explanation...(Derive the equation)
 
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Hi abhineetK! :wink:

Show us what you've tried, and where you're stuck, and then we'll know how to help! :smile:
 
\deltaP=Pocos(\omegat-kx) ...(1)

B=-\deltaP/(\DeltaV/V) ...(2)

\rho=m/V

=>\partial\rho=-(m/V2)\partialV

=>\partial\rho=-\rho(\partialV/V)

=>\partial\rho/\rho=-\partialV/V

=>\partial\rho/\rho=\deltaP/B [using (2)]

=>\partial\rho=(\rho.Po/B)cos(\omegat-kx) [using (1)]
Is it correct?
 

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