My study topic is jet mixing noise. I am given a velocity field in Vx, Vy, Vz at x and y coordinates, and would like to find the pressure field, and from that, find the sound level (or at least something related to sound). How should I proceed?
Dear Omkar Vaidya
The forward problem is knowing the p field ---> one finds the v field, in that case:
First, we need to establish under which thermodynamical conditions you want to calculate the v field from field p(x,y,z).
Second, use an initial value p0, and calculate the derivate of the pressure field with respect to the density of particles around that initial value.
Third, one gets the "sound" v field components.
You are asking the inverse problem, from v field, you want the p field,
v field ---> p field:
Article Sound field separation with sound pressure and particle velo...
In linear acoustics, sound pressure and particle velocity are related through Euler's equation (second Newton's law for fluids). However, since you are studying jet mixing noise, the noise generation process is much more complex. The result depends on several variables such as jet temperature, flow velocity (Mach number, Reynolds number, subsonic/supersonic, turbulent jets, etc.). Some researchers have used either Lighthill's acoustic analogy or numerical CFD techniques to approach this problem. Once you get the sound pressure field, you may obtain the sound pressure amplitude at point (x,y) by taking the absolute value of the complex pressure. Then, you can obtain the RMS sound pressure, prms, (for example, dividing by sqrt(2) for pure tone), and the sound pressure level Lp=20log(prms/pref), where pref = 2x10^-5 N/m2 (20 micropascals).
To begin with, try to solve a much simpler problem - generating sound in an organ pipe ;-)
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