Quadrupole Point Source
Use the Quadrupole Point Source node to enter a quadrupole point source. A quadrupole is mathematically a source that corresponds to two dipoles close to each other. A complex acoustic source may be expanded and approximated by a collection of point sources (Monopole Point Source, Dipole Point Source, and Quadrupole Point Source). The quadrupole point source adds a point source term to the right-hand side of the governing Helmholtz equation such that:
where is the delta function in three dimensions and adds the source at the point where x = x0. The quadrupole D-vector D (SI unit: N) and the quadrupole d-vector d (SI unit: m) depend on the source type selected, as discussed below. In 2D axisymmetric models the quadrupole point source is only added to the z-axis, such that x0 = (0,0,z) and only orientations along the axis are possible. Two types of predefined quadrupole sources exist, a Power (longitudinal) and a Power (lateral) configuration, respectively. In the longitudinal source the D and d vectors are parallel and point in the same direction. In the lateral configuration the D and d vectors are perpendicular to each other, see Ref. 5 for details.
Quadrupole Point Source
Select a Type: Power (longitudinal) (the default), Power (lateral), or User defined. The lateral options does not exist in 2D-axisymmetric models.
User Defined
For User defined enter the Quadrupole d vector (SI unit: m) and Quadrupole D vector (SI unit: N). In 2D axisymmetric models enter a Quadrupole amplitude Q (SI unit: N⋅m) as both the D and d vectors are pointed along the z-axis.
Figure 2-2: Schematic illustration of the user defined quadrupole point source.
Power (longitudinal)
The Power (longitudinal) defines the following values for the two quadrupole vectors
Enter the following:
•
Free space reference power (RMS), Prms (SI unit: W). In a homogeneous medium the specified power is radiated (the reference), but with other objects and boundaries present the actual power is different.
•
The source Phase (SI unit: rad).
•
Quadrupole direction, (dimensionless). In a 2D axisymmetric model the direction is along the z-axis.
Figure 2-3: Schematic illustration of the longitudinal power quadrupole point source.
Power (lateral)
The Power (lateral), not defined in 2D axisymmetric components, defines the following values for the two quadrupole vectors
Enter the following:
•
Free space reference power (RMS), Prms (SI unit: W). In a homogeneous medium the specified power is radiated (the reference), but with other objects and boundaries present the actual power is different.
•
The source Phase (SI unit: rad).
•
Quadrupole normal, n (dimensionless). This is the normal to the plane in which the quadrupole is located.
•
Quadrupole direction, (dimensionless). The projection of this vector onto the plane (defined by the normal n) defines the direction of the dipole D-vector.
Figure 2-4: Schematic illustration of lateral quadrupole point source.
Point sources in 2D components also exist. They actually correspond to infinite out-of-plane line sources, see Point Sources for 2D Components.