Density equation of sound wave

[abhineetK]

Let pressure equation of sound wave be
$$\Delta$$p=P_ocos($$\omega$$t-kx), then
what will be the density equation of the sound wave?
give your answer with proof and proper explanation...(Derive the equation)

 

[tiny-tim]

Hi abhineetK!

Show us what you've tried, and where you're stuck, and then we'll know how to help!

 

[abhineetK]

$$\delta$$P=P_ocos($$\omega$$t-kx) ...(1)

B=-$$\delta$$P/($$\Delta$$V/V) ...(2)

$$\rho$$=m/V

=>$$\partial\rho$$=-(m/V²)$$\partial$$V

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

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

=>$$\partial\rho$$/$$\rho$$=$$\delta$$P/B [using (2)]

=>$$\partial\rho$$=($$\rho$$.P_o/B)cos($$\omega$$t-kx) [using (1)]
Is it correct?