Calculate acoustic pressure from velocity potential

[SFB]

Hi

I solved the helmholtz equation
$$\Delta\Phi+k^2\Phi=0$$

to find the velocity potential in the cylindrical resonator. Since my answer is only a function of radius r and independent of time t, how can I find the acoustic pressure? what is the formula ?

I know the formula
p=-density* $$\frac{d\phi}{dt}$$

but I am not sure whether this would give the right answer as $$\phi$$ is no longer a function t.

Fourier transform of the first equation gives me a time independant equation but it was in the complex form?Any suggetsion would be very helpful.

Thanks

 

[LightHero]

.The equation you solved is a Helmholtz equation, which is a type of wave equation that describes the propagation of sound in a medium. The pressure at any given point is related to the velocity potential via the equation you provided: p=-density* \frac{d\phi}{dt}. Since your solution is independent of time, this equation reduces to: p=-density* \frac{d\phi}{dr}. This is the equation you need to use to calculate the acoustic pressure at any given point in the cylindrical resonator.