Research On The Acoustic Impedance

Question:

Discuss the effects of the material acoustic interference on two main scenarios.

Answer:

Introduction

Acoustics is the process of propagating small sound pressure waves through a medium.

Researchers have long been interested in the topic, as they try to uncover the secrets of this phenomenon.

Acoustic impedance is one of the topics that researchers have concentrated their energy on to improve the concept. This was done in order to discover how and why it occurs for each material.

These are just a few of the many applications and methods that have been explored.

Classical deterministic mathematical models are used often to mathematically create a scenario for acoustic resistance and how it depends upon frequency.

Two methods will be presented in this paper that include practical applications. They are the ultrasound with spatial compounding applications.

These methods have two main applications.

The purpose of this paper is to present the principles and practice of studying acoustic imperceptibility.

This paper will serve as a substantial resource for the practical application of the acoustic impedance theory in the real world.

Methods to measure Acoustic Impedance

2-Microphone Transfer Function

This method uses an impedance tub with two microphones at locations that are known to be far apart.

The principle is: A loudspeaker propagates an incident wave and produces a reflected result.

The standing-wave phenomenon is then used to measure various characteristics, such as impedance and wavelength.

It is important to note that the tube was installed in situ during the setup.

The frequency of the plane waves is determined by the geometry of the tube, such as its diameter and speed in air.

Chalmers (2012) explains that the upper limit frequency must be mathematically:

The speaker acts as a source of sound waves, and the incident pressure wave will be denoted PR

Notably, the microphone position has a complex sound pressure.

The microphone would then pick up the signals (both incident and reflected pressure waves).

To minimize the mismatch between microphones and their internal amplitudes and phases, however, the microphone interchange technique can be used (Chalmer (2012)).

Finally, you can calculate the transfer function for both incident and reflecting waves between microphones using the general equations 3,(a) or 3,(b).

Where s=x2-x1

You can then determine the reflection coefficient (which is the ratio of complex incident and reflected pressures).

It is worth noting that the incident propagating wave is not always reflected, but absorbed. This is called:

A = 1-/R/2 ….

Surface acoustic resistance is thus:

Zs=Z1+R/(1–R) where Zo=PoCo acoustical impedance of the air

Effect of frequency on the impedance

Source frequency affects the acoustical imperance. Therefore, low frequency sources will result in lower impedance intensity and thus a lower impedance level.

As shown by equation 1, the best performance of the setup is achieved at a specific low frequency area.

A key factor in the frequency range of the method is the tube diameter.

The tube diameter can limit the frequency of higher frequencies beyond the limits.

Wave Decomposition Method

Since the previous method was limited to plane waves, the model is only applicable to certain applications.

Wave decomposition can be applied to normal pressure waves as well as the oblique incident. This makes it more applicable to higher modal orders modes (Schultz Cattafesta and Sheplak 2006).

The method depicts an unlined duct with an impedance border on one side and an excitation sounder at the other.

The material is usually inserted at duct-end so that the material, in part, produces a reflective and reactive boundary during propagation. This results in complex transfer functions.

Where k= complex audio impedance

C= Sonic Wave Speed in the Duct (m/s).

t = time variable

x= Spatial variable (m).

L= length of duct (m).

Equation 2 shows, therefore, how the impedance can determined by the method after the experiment has been completed:

The spatial derivative of the particle displacement determines the acoustic tension of the system.

Acoustic Impedance

The Turbofan Engine Acoustic

Turbofan engines can use the two microphone transfer function method to analyze the material audio of the compressors and turbines.

The model assumes that the phenomenon is occurring in lined conduits with an axial flow sound pressure waves.

The boundary conditions at the walls as well as at the treatment surfaces are important (Malmary & Carbonne (2002).

Malmary & Carbonne, 2001 give the following normalized acoustic resistance:

Zt= 1/PoCox x (P/v’n’ ….

where P= acoustic tension at a point on the liner surface, v= acoustic speed at the same place, n= normal to liner surface, Co=speed sound in the air and?=air density

A part of the layer impedance must be taken into account. The total acoustic resistance from the system will be given by:

K= Acoustic wave number, K=w/co & L= Cavity depth

Critical parameters that will affect the usefulness of the model are: The dimensional property of attenuating material and flow characteristics like frequency and mach number.

Where w= is sound pulsation

/v/= The amplitude of the normal audio velocity

M= Flow Mach Number

The frequency characteristic is correlated with the acoustic impenetrance in the following linearized model:

First, perforated pipes, Malmary & Carbonne (2001), indicate the impedance as Z= r+jX 4.

Where r=8vw)0.5/Co(1+e/d),+1/8

This model, however, is not complete as it was mentioned previously. Because real-world acoustic systems often display non-linear behavior, a further extension of the method is required.

But, there are many other ways to utilize the acoustic interference phenomenon as well as their underlying applications.

Acoustic impedance measurements may be used more frequently in the generation ultrasound images. However problems such as occlusions could hinder the performance when the material’s acoustic impermeance is high.

The other scenarios where the average impedance can be used straight away, however, require that the beam intensity is increased in order to overcome material impedances.

This is known as spatial compounding.

This will allow the system to take root.

However, spatial compounding makes it possible to achieve excellent results while overcoming any layer impedances in the propagation process (Malmary & Carbonne 2001).

Refer to

Dingzeyu L, David, I Matusik, W & Changxi Zheng C. (2016).

Acoustic Voxels – Computational Optimization Modular Acoustic Filters.

Acoustic impedance measurement with the grazing stream.

An introduction to Acoustics.

Eindhoven University of Technology.

Wachinger C. Shams R. & Navab N. (2008).

Estimation of Acoustic Imperance from Multiple Ultrasound Images. Application to Spatial Compoundeding.

Evaluation of impedance tubes methods – Two microphone in-situ method to evaluate road surfaces, and three microphone transfer function method to evaluate porous materials.

A transfer function method to determine characteristic impedance of porous materials and their propagation constant.

Acoustic Impedance Measurement System using 2 microphones.

Acoustic Measurements.

Acoustic Impedance Measurements.

Modal decomposition method of acoustic resistance testing in square conduits.

Comparison of Acoustic Impedance Measuring Techniques.

Acoustic Impedance Measurements

Spatial Compounding and Frequency Compounding in the Application to Attenuation Evaluation in Tissue Ziemowit KLIMONDA JerzyLITNIEWSKI Piotr KARWAT Andrzej NOWICKI Institute of Fundamental Technological Research Polish Academy of Science

Chapter 3 –Basic Acoustic Modeling.

Acoustic Impedance

Evaluation of impedance tube techniques – A two microphone method in-situ for road surfaces and the three-microphone transfer function method porous material Masters Thesis in Master’s program in Sound and vibration.

Chalmer University of Technology.

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