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| Project 2: Conclusion |
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| In qustion one, the equations for the dipole source were found by using trig equations from the diagram in the notes. There are two identical point sources, Q1 and Q2 that are out of phase by 180 degreees. So we can call Q2=-Q1, this is how I changed the beam pattern of 1+Q2/Q1exp(j*k*h*sin(thetaN) = 1-exp(j*k*h*sin(thetaN). For the particle displacement plots I used P1=[(j*w*rho)/(4*pi*R)]*exp(-j*k*R), yet I neglected the constant term to get P1=[1/R]*exp(-j*k*R). And then used Euler's equation to neglect the imaginary part: P1=[1/R]*cos(k*R). But since there were two sources I had a P1 with a radius of R and a P2 with a radius of r. These were both found by creating the hypotenuse in the X,Y plan, considering h to be the distance between the sources.. So r=sqrt(X^2+(Y+h/2)^2) and R=sqrt(X^2+(Y-h/2)^2). Pfar was created by Pfar1=P1*beam pattern and Pfar2=P2*beam pattern. Finally the 3-D plot was made by plotting X,Y, and Pfar2-Pfar1. For the piston and directional array plots, a very similar process was done. Although, different equations were considered for each case. For example, in a piston plot there is only one source and therefore one radius to consider. This project was very helpful by giving me visual representation of loundspeaker arrays and the formulas to obtain them. |
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