Related Experiment Video
Updated: Jul 7, 2026
08:51
Statistical Modelling of Cortical Connectivity Using Non-invasive Electroencephalograms
Published on: November 1, 2019
Reciprocal relations for transmission coefficients: theory and application.
J Qu1, J D Achenbach, R A Roberts
1Dept. of Mech. Eng. and Appl. Mech., Pennsylvania Univ., Philadelphia, PA.
Summary
This study proves reciprocity relations for wave transmission between fluids and anisotropic solids. These relations enable calculating solid-fluid acoustic properties from measured transmission data.
Area of Science:
- Acoustics
- Solid Mechanics
- Wave Propagation
Background:
- Reciprocity principles are fundamental in physics.
- Understanding wave interactions at fluid-anisotropic solid interfaces is crucial for material characterization.
Purpose of the Study:
- To rigorously derive and validate reciprocity relations for acoustic wave transmission.
- To demonstrate the application of these relations for determining fluid-solid acoustic coefficients.
Main Methods:
- Derivation of reciprocity relations based on the elastodynamics reciprocity theorem.
- Experimental measurement of transmission coefficients for a composite material slab.
- Comparison of experimental data with theoretical predictions.
Main Results:
- Precise forms of reciprocity relations for transmission coefficients and energy fluxes were established.
- The derived relations successfully allowed calculation of water-solid coefficients.
- Experimental results showed good agreement with theoretical values.
Conclusions:
- The study provides a theoretical framework for acoustic wave reciprocity.
- The findings offer a practical method for characterizing anisotropic solids using wave transmission measurements.
More Related Videos
Related Concept Videos
01:26Transmission-Line Differential Equations
Transmission lines are essential components of electrical power systems. They are characterized by the distributed nature of resistance (R), inductance (L), and capacitance (C) per unit length. To analyze these lines, differential equations are employed to model the variations in voltage and current along the line.
Line Section Model
A circuit representing a line section of length Δx helps in understanding the transmission line parameters. The voltage V(x) and current i(x) are measured from the...
Line Section Model
A circuit representing a line section of length Δx helps in understanding the transmission line parameters. The voltage V(x) and current i(x) are measured from the...
01:21Boundary Conditions: Lossless Lines
Consider a single-phase, two-wire, lossless transmission line terminated by an impedance at the receiving end and a source with Thevenin voltage and impedance at the sending end. The line, with length, has a surge impedance and wave velocity determined by the line's inductance and capacitance.
At the receiving end, the boundary condition states that the voltage equals the product of the receiving-end impedance and current. This relationship is expressed as a function of the incident and...
At the receiving end, the boundary condition states that the voltage equals the product of the receiving-end impedance and current. This relationship is expressed as a function of the incident and...
01:20The Maximum Power Transfer Theorem
Consider a linear AC Thevenin equivalent circuit connected to a load impedance.
The load connected draws the current, and the circuit delivers the power to the load. The alternating current flowing through the load is determined using the rectangular form of voltages, currents, network impedance, and load impedance. The average power delivered to the load is obtained from the product of the square of current and load resistance.
The load connected draws the current, and the circuit delivers the power to the load. The alternating current flowing through the load is determined using the rectangular form of voltages, currents, network impedance, and load impedance. The average power delivered to the load is obtained from the product of the square of current and load resistance.
01:21Transfer Function in Control Systems
The transfer function is a fundamental concept in the analysis and design of linear time-invariant (LTI) systems. It offers a concise way to understand how a system responds to different inputs in the frequency domain. It serves as a bridge between the time-domain differential equations that describe system dynamics and the frequency-domain representation that facilitates easier manipulation and analysis.
To derive the transfer function, consider a general nth-order linear time-invariant...
To derive the transfer function, consider a general nth-order linear time-invariant...
01:25Network Function of a Circuit
Frequency response analysis in electrical circuits provides vital insights into a circuit's behavior as the frequency of the input signal changes. The transfer function, a mathematical tool, is instrumental in understanding this behavior. It defines the relationship between phasor output and input and comes in four types: voltage gain, current gain, transfer impedance, and transfer admittance. The critical components of the transfer function are the poles and zeros.
01:12Bewley Lattice Diagram
The Bewley lattice diagram, developed by L. V. Bewley, effectively organizes the reflections occurring during transmission-line transients. It visually represents how voltage waves propagate and reflect within a transmission line, making it easier to understand the complex interactions that occur.