Modelling a Low freq Dipole Using exact and approximate formulation

[mogley76]

Homework Statement

consider s dipole with spacing of 2cm between the two sources. it is radiating a 100hz pure tone, and the magnitude of each source 'A' is given by 1n/M^2.
calculate the pressure as a function of the angle between the reciever and the dipole for a reciever 10 m from the dipole centre, plot graphs of rms vs angle and pressure vs angle using both approximate and exact equations.

Homework Equations

exact: p(r)=p1(r1) + p2(r2) = A/r1 e^-j(kr1) - A/r2 e^-j(kr2)

approx: modulus of p(θ,r) ≈ (2AKd *modulus of sin(θ) )/r

The Attempt at a Solution

i plotted these in MATLAB but there was a small difference between the two plots obtained from the formulations which i can't work out, the exact formulation was slightly bigger than the approximate one. can anyone explain to me please?

 

[mark726]

There could be several reasons for the difference between the plots obtained from the exact and approximate formulations. Some possible explanations could be:

1. The approximation used in the approximate formulation may not be accurate enough for the given scenario. This could lead to a discrepancy between the two plots.

2. The exact formulation may have some assumptions or simplifications that are not present in the approximate formulation. These differences could lead to variations in the resulting plots.

3. There could be errors in the implementation of the equations in MATLAB. It is important to double-check the code and make sure that all the necessary parameters and variables are included correctly.

4. The values used for the parameters (such as the distance from the dipole, frequency, and magnitude of the sources) may not be exactly the same in both formulations. Even small variations in these values can result in differences in the plots.

It is also worth noting that the exact formulation is likely to be more accurate than the approximate one. Therefore, it is expected that the plots obtained from the exact formulation will be slightly different from those obtained from the approximate formulation. However, if the difference is significant, it is important to carefully examine the above factors to determine the cause of the discrepancy.