Question

deduce an expression for newton's formula related to speed of sound and discuss the correction to this forlmul made by laplace

Answer 1

$$\begin{gathered} PV=cons\tan t \\ P∆V+V∆P=0 \\ B=\frac{-∆P}{∆V/V}=P \\ VelocityofSound,v=\sqrt{\frac{P}{\rho }} \\ InthisEquationLaplacesuggestedthepropagationofSoundinnotIsothermalprocessbutisisAdiabatic. \\ P{V}^{\gamma }=cons\tan t \\ taking\log ,\ln P+\gamma \ln V=con\tan t \\ \frac{∆P}{P}+\gamma \frac{∆V}{V}=0 \\ B=\frac{-∆P}{∆V/V}=\gamma P \\ \Rightarrow velocityofsound,v=\sqrt{\frac{\gamma P}{\rho }} \end{gathered}$$