Manual on the Code of the Book Entitled “Acoustic Waves Generated by Parametric Array Loudspeakers”

Jiaxin Zhong
(May 15, 2024)

1 Introduction

This document introduces the usage of the code package, which is a supplementary material for the book “Acoustic Waves Generated by Parametric Array Loudspeakers”. All demos and functions were tested by MATLAB R2022b installed on a personal computer with an AMD Ryzen Threadripper 3960X central processing unit (CPU) with 256 GB of random access memory (RAM).

1.1 Installation


  1. 1.

    Download all codes from GitHub: JiaxinZhong/AWPAL

  2. 2.

    Run the script AWPAL.m at first to add subfolders to the path.

2 Demo Scripts and Core Functions

2.1 Direct Integration Method (DIM)

2.1.1 Ultrasound Field General Solution
Function: DIM3D.m

The calculation utilizes the Rayleigh integral reading that [1, Eq. (2.39)]

pi(𝐫)=ρ0ωi2πivi,z(𝐫s)eiki|𝐫𝐫s||𝐫𝐫s|d2𝐫s. (1)

2.1.2 Audio Sound Field General Solution

2.1.3 Function: PalDIM3D.m

pa(𝐫)=βωa24πρ0c04p1(𝐫v)p2(𝐫v)|𝐫𝐫v|eika|𝐫𝐫v|d3𝐫v. (2) On-Axis
Demo: PalDIM3D_CircSrc_Axis_Demo.m

Figure 1 is generated by this demo file. The data is stored in file PalDIM3D_CircSrc_Axis_Demo_Uniform.mat.

Refer to caption
Figure 1: On-axial SPL (dB) as a function of the axial distance (z, m) [2, Fig. 2(d)]. The PAL has a circular uniform profile with a radius of a=0.1m.

Figure 2 is generated by this demo file. The data is stored in file PalDIM3D_CircSrc_Axis_Demo_Focus.mat.

Refer to caption
Figure 2: On-axial SPL (dB) as a function of the axial distance (z, m) [2, Fig. 2(e)]. The PAL has a focusing profile with a focal distance of rf=0.2m. The radius of the PAL is a=0.1m.
Function: PalDIM3D_CircSrc_Axis.m

Calculate the audio sound field on the axis ρ=0 using the DIM. The source profile is assumed to be axisymmetric in the azimuthal direction, i.e., vi,z(𝐫s) is independent of φs. The formula used in this function is

pa(ρ=0,φ,z)=βωa22ρ0c040p1(𝐫v)p2(𝐫v)ρv2+(zzv)2eikaρv2+(zzv)2ρvdρvdzv (3)

2.2 Spherical Wave Expansion (SWE)

2.2.1 Function: SWE3D_RadialInt.m


r1r2jn(kr<)hn(kr>)rsdrs (4)

where r<=min(r,rs) and r>=max(r,rs).

3 Summary of Equations

3.1 Source Profile

The focusing profile reads

vi,z(𝐫s)=v0exp(i(ki)|𝐫f𝐫s|). (5)

where 𝐫f denotes the location of the focal point.

4 Known Issues


  • [1] J. Zhong and X. Qiu (2024) Acoustic waves generated by parametric array loudspeakers (to be published). CRC Press. Cited by: ¶
  • [2] J. Zhong, T. Zhuang, R. Kirby, M. Karimi, X. Qiu, H. Zou, and J. Lu (2022) Low frequency audio sound field generated by a focusing parametric array loudspeaker. IEEE/ACM Trans. Audio Speech Lang. Process. 30, pp. 3098–3109. External Links: ISSN 0001-4966, Document Cited by: Figure 1, Figure 2.