# A Green’s Function for Acoustic Problems in Pekeris Waveguide Using a Rigorous Image Source Method

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Theoretical Model of the Rigorous ISM

## 3. Theoretical Model Verification

^{3}and ${c}_{a}$ = 1500 m/s, respectively. The seabed in the Pekeris waveguide is regarded as an infinite half-space liquid with the density and the sound speed of ${\rho}_{b}$ = 2000 kg/m3 and ${c}_{b}$= 1800 m/s, respectively, and the sound absorption in the seabed is also considered. The depth of each receiver is ${z}_{i}$ and the horizontal interval is 1 m.

## 4. Conclusions and Future Work

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Schematic diagram of the Green’s function (GF) in shallow water: (

**a**) the principle of the rigorous image source method (ISM); (

**b**) sound reflection of spherical waves on the liquid–liquid interface.

**Figure 2.**Diagram of the interaction between plane wave and liquid–liquid interface: (

**a**) decomposition of the wavenumber vector k in three-dimensional (3D) space; (

**b**) sound reflection of plane waves on the liquid–liquid interface.

**Figure 4.**Curves of plane wave reflection coefficients versus angle of incidence for different absorptions.

**Figure 5.**Sound field comparison between near- to far-field model and theoretical solution: (

**a**) f = 25 Hz; (

**b**) f = 50 Hz; (

**c**) f = 100 Hz; (

**d**) f = 200 Hz. SPL: sound pressure level; WI: wavenumber integration method.

**Figure 6.**The SPL comparison of the GF with different frequencies: (

**a**) f = 25 Hz, WI; (

**b**) f = 25 Hz, the presented method; (

**c**) f = 100 Hz, WI; (

**d**) f = 100 Hz, the presented method.

n | 1 | 2 | 3 | 4 | 5 | 6 |
---|---|---|---|---|---|---|

${f}_{n}$/Hz | 6.78 | 20.35 | 33.92 | 47.49 | 61.06 | 74.62 |

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**MDPI and ACS Style**

Qian, Z.; Shang, D.; Hu, Y.; Xu, X.; Zhao, H.; Zhai, J.
A Green’s Function for Acoustic Problems in Pekeris Waveguide Using a Rigorous Image Source Method. *Appl. Sci.* **2021**, *11*, 2722.
https://doi.org/10.3390/app11062722

**AMA Style**

Qian Z, Shang D, Hu Y, Xu X, Zhao H, Zhai J.
A Green’s Function for Acoustic Problems in Pekeris Waveguide Using a Rigorous Image Source Method. *Applied Sciences*. 2021; 11(6):2722.
https://doi.org/10.3390/app11062722

**Chicago/Turabian Style**

Qian, Zhiwen, Dejiang Shang, Yuan Hu, Xinyang Xu, Haihan Zhao, and Jingsheng Zhai.
2021. "A Green’s Function for Acoustic Problems in Pekeris Waveguide Using a Rigorous Image Source Method" *Applied Sciences* 11, no. 6: 2722.
https://doi.org/10.3390/app11062722