An Introduction to Virtual Sound Barriers

Xiaojun Qiu

• Publisher: CRC Press
• Year: 2019
• ISBN:
  9781351168021
• Edition: 1
• Topic: Technology & Engineering
• Subtopic: Acoustical Engineering
• Index: Technology & Engineering

A virtual sound barrier is an active noise control system that uses arrays of loudspeakers and microphones to create a useful size of quiet zone and can be used to reduce sound propagation, radiation, or transmission from noise sources or to reduce noise level around people in a noisy environment. This book introduces the history, principle, and design methods of virtual sound barriers first, and then describes recent progress in research on the systems. Two virtual sound barrier systems, i.e., planar virtual sound barrier system and three-dimensional virtual sound barrier system, are discussed including applications, limitations and future direction discussions.

1

Introduction

1.1 Sound Propagation

Sound is a longitudinal mechanical wave, where the displacement of the medium at each point is normal to the local wave-front surface when the disturbance is traveling in a medium (Morfey, 2001). Sound speed is different in different mediums, in air under normal atmosphere pressure at 20°C, the sound speed is approximately 343 m/s. There is usually an energy loss when sound propagates in a medium. For example, when a sound wave propagates in porous materials the porous gas-filled medium can be treated as an equivalent uniform medium for analysis purposes. So a propagation factor e^jωt−γx can be used to describe the dependence of the propagating wave on time t and the propagation coordinate x (Bies, Hansen, and Howard, 2018). Here, ω = 2πf is the angular frequency and f is the wave frequency. The propagation constant γ is also called the propagation coefficient, which is a complex number that can be represented by,

$$\gamma =\sigma +jk$$

(1.1)

where the propagation wave number k = ω/c is also called the phase coefficient, σ is called the attenuation coefficient, and c is the speed of sound in the medium. Although the energy loss can be caused by some kinds of energy dissipation, such as absorption, the term “attenuation coefficient” is used in this book to describe the reduction in amplitude of a progressive wave with the distance in the propagation direction in the medium by e^−σx. This coefficient is the amplitude attenuation coefficient instead of the energy attenuation coefficient.

The attenuation of a propagating sound caused by air can usually be neglected in the low-frequency range. For example, the sound pressure level attenuation is about 1 dB for a sound wave at 250 Hz traveling over 1000 m; however, for a sound wave at 4000 Hz, the attenuation can be from 24 dB to 67 dB depending on the temperature and humidity of the air (Bies, Hansen, and Howard, 2018). In the sound propagation prediction scheme, this sound absorption factor is usually considered separately, so it is not included in the discussion of the sound barriers in this book.

1.1.1 Sound Absorption and Absorption Coefficient

When a propagating sound wave encounters a different medium or space discontinuity in the media, reflection, diffraction, and/or transmission of waves occur, where the incident wave arriving at the boundary interacts with it to produce waves traveling away from the boundary (Morfey, 2001). The reflected wave or scattered waves follow certain rules. For example, for the specular reflection in which a plane incident wave is reflected by a uniform plane boundary, the normal wave number component of the incident field is reversed on reflection, and the wave number component parallel to the boundary is unaltered, so the angle of reflection is equal to the angle of incidence. Figure 1.1 summarizes the relationships of different kinds of energy when a propagating wave is incident upon a layer of porous material. The total input energy brought from the incident wave is E _i, which is equal to the summation of E _r, E _s, E _a and E _t, i.e., the energy reflected and scattered from the boundary, the energy dissipated inside the porous material layer, and the energy transmitted through the layer.

FIGURE 1.1
Sound reflection, scattering, absorption, and transmission when a propagating sound wave encounters a layer of porous material.

There is usually an energy loss when a sound is reflected from a boundary, and the changes in amplitude and phase that take place during the reflection can be represented by the complex reflection factor or sound pressure reflection coefficient as

$$R=\frac{p_{\text{r}}}{p_{\text{i}}}$$

(1.2)

where p _r and p _i are the complex amplitudes o...