亥姆霍兹方程
横截面(物理)
背景(考古学)
二次增长
数学分析
波动方程
领域(数学)
亥姆霍兹自由能
物理
章节(排版)
声波
反射(计算机编程)
数学
声学
边值问题
计算机科学
地质学
热力学
量子力学
古生物学
纯数学
操作系统
程序设计语言
作者
Michal Bednařı́k,Milan Červenka
标识
DOI:10.1016/j.apm.2023.09.005
摘要
In this study, a rectangular cross-section sonic black hole (SBH) is explored and a one-dimensional model equation for the acoustic field inside it is presented. The model equation's applicability is verified through a comparison with the corresponding two-dimensional Helmholtz equation. A general analytical solution, which takes into account the SBH's quadratically varying internal cross-section, is derived using linearly independent confluent Heun functions. To investigate the acoustic wave behavior in the SBH, the wave splitting method is utilized to obtain forward and backward acoustic pressure waves, and the reflection coefficient is calculated. To confirm the validity of the analytical solution, a comparison is made with numerical results obtained from the Riccati equation. Within the context of this study, a detailed discussion is provided regarding the applicability of the analytical solution.
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