# Analysis and Application of Screens for Acoustic Impedance in a Speaker Box with a Passive Radiator to Decrease Standing-Wave Influence

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## Abstract

**:**

## 1. Introduction

## 2. Analysis Method

#### 2.1. Electromagnetic Modeling

_{E}, L

_{E}, V and i are the electrical voice-coil resistance, the voice-coil inductance, the voltage, and the current.

#### 2.2. Mechanical Modeling

_{ms}is the mechanical mass of the vibration system which includes the driver diaphragm, suspension, and coil, R

_{m}

_{s}the mechanical resistance of the total-driver losses, and C

_{ms}the mechanical compliance of the driver suspension.

#### 2.3. Acoustic Modeling

_{0}the background density, $\dot{X}$ the node velocity, and c the sound velocity. In addition to the governing equation, there is boundary condition to solve the governing equation. The impedance boundary condition describes the pressure drop across the boundary to the velocity at the boundary.

_{i}is the acoustic impedance, which is the ratio between the pressure drop and the normal particle velocity. There are two opposite limits. One is that acoustic impedance becomes zero. The other is that acoustic impedance becomes infinite. This boundary condition is identical to the sound hard and sound soft boundary conditions, respectively. The surface of speaker and speaker box are treated as rigid wall, which means the acoustic impedance is infinite. The acoustic impedance of air in the enclosure is zero. ρ

_{c}, p

_{t}, q

_{d}, p

_{t},

_{left}and p

_{t},

_{right}are the density of air, sound pressure of air, zero dipole source, acoustic pressure on the left and right surface.

#### 2.4. Electromagnetic-Mechanical-Acoustic Coupling

#### 2.4.1. Electromagnetic–Mechanical Coupling

#### 2.4.2. Mechanical–Acoustic Coupling

_{lower}and F

_{upper}, respectively. F

_{lower}and F

_{upper}are obtained by integrating the node pressure force over the diaphragm surface. The difference between the lower part and upper part air pressures is defined as F

_{air}. The air-pressure force is depicted in Figure 5. In addition, a current force drives the unit, except for the air-pressure force. This current force is defined as F

_{current}. The total force acting on the vibration system is F. It is concluded that the total force influences the mechanical velocity. Therefore, the mechanical and acoustic domains are considered to be coupled with each other.

## 3. FEM Modeling of Standing Wave

_{x}, n

_{y}, and n

_{z}are the integers for the corresponding resonance modes; l

_{x}, l

_{y}, and l

_{z}are the lengths of the enclosure in the x, y, and z directions, respectively; and c is the air velocity. Thus, the resonance frequency of the standing wave is related to the dimensions of the speaker box. The resonance decreases with increase in speaker-box dimensions.

## 4. Experiment

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Abbreviations

SPL | Sound pressure level |

FFT | Fast Fourier transform |

DOF | Degree of freedom |

EMF | Electromotive force |

FEM | Finite element method |

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Item | Driver | Passive Radiator |
---|---|---|

R_{E} (Ohm) | 6.58 | 0 |

L_{E} (mH) | 0.038 | 0 |

M_{ms} (g) | 0.9 | 0.638 |

R_{ms} (kg/s) | 0.1 | 0.12 |

C_{ms} (mm/N) | 1.11 | 0.278 |

Bl (N/A) | 0.161 | 0 |

Item | Value |
---|---|

Acoustic impedance (MKS Rayls) | 145 |

Thickness [µm] | 72 (+4/−3) |

Weight [g/m^{2}] | 53 (+2/−3) |

Open Area [%] | 14 (+1/−2) |

Pore Size [µm] | 27 (+/−2) |

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## Share and Cite

**MDPI and ACS Style**

Jiang, Y.-W.; Xu, D.-P.; Jiang, Z.-X.; Kim, J.-H.; Park, K.-H.; Hwang, S.-M.
Analysis and Application of Screens for Acoustic Impedance in a Speaker Box with a Passive Radiator to Decrease Standing-Wave Influence. *Appl. Sci.* **2020**, *10*, 866.
https://doi.org/10.3390/app10030866

**AMA Style**

Jiang Y-W, Xu D-P, Jiang Z-X, Kim J-H, Park K-H, Hwang S-M.
Analysis and Application of Screens for Acoustic Impedance in a Speaker Box with a Passive Radiator to Decrease Standing-Wave Influence. *Applied Sciences*. 2020; 10(3):866.
https://doi.org/10.3390/app10030866

**Chicago/Turabian Style**

Jiang, Yuan-Wu, Dan-Ping Xu, Zhi-Xiong Jiang, Jun-Hyung Kim, Ki-Hong Park, and Sang-Moon Hwang.
2020. "Analysis and Application of Screens for Acoustic Impedance in a Speaker Box with a Passive Radiator to Decrease Standing-Wave Influence" *Applied Sciences* 10, no. 3: 866.
https://doi.org/10.3390/app10030866