Related Experiment Video
Updated: Feb 13, 2026

Thermochemical Studies of NiII and ZnII Ternary Complexes Using Ion Mobility-Mass Spectrometry
Published on: June 8, 2022
Inducing a nonreflective airborne discontinuity in a circular duct by using a nonresonant side branch to create mode
Yongxiong Xiao1, Huancai Lu1, D Michael McFarland1
1Sound and Vibration Laboratory, College of Mechanical Engineering, Zhejiang University of Technology, 18 Chaowang Road, Hangzhou 310014, China.
Abstract:
A nonreflective airborne discontinuity is created in a one-dimensional rigid-walled duct when the mode complexity introduced by a nonresonant side branch reaches a maximum, so that a sound wave can be spatially separated into physical regions of traveling and standing waves. The nonresonance of the side branch is demonstrated, the mode complexity is quantified, and a computational method to optimize side-branch parameters to maximize mode complexity in the duct in the presence of three-dimensional effects is presented. The optimal side-branch parameters that maximize the mode complexity and thus minimize reflection are found using finite element analysis and a derivative-free optimization routine. Sensitivity of mode complexity near the optimum with respect to side-branch parameters is then examined. The results show reflection from the impedance discontinuity in the duct can be reduced nearly to zero, providing a practical means of achieving a nonreflective discontinuity for a plane wave propagating in a duct of finite length.
Related Concept Videos
Limits with Oscillating Discontinuities
Improper Integrals: Discontinuous Integrands
What is a Mode?
There can be more than one mode in a data set if multiple values have the same highest frequency. For instance, suppose that the Statistics exam scores of 20 students are: 50; 53; 59; 59; 63; 63; 72; 72; 72; 72; 72; 76; 78; 81; 83; 84; 84; 84; 90; 93. Here, the mode is 72, as it occurs most frequently, five times.
A data set with two modes is called bimodal. For example,...
Ventilatory Modes
There are three ventilatory modes: full support, partial support, and spontaneous. These are described below.
Full Support Modes
Full support modes include controlled mechanical ventilation, continuous mandatory...
Deformation in a Circular Shaft
Transmission-based Precautions II: Airborne and Protective Environment
Airborne precautions:
Use airborne precautions when treating patients known or suspected to have diseases that spread through the air—for example, tuberculosis or measles. These organisms are present in smaller droplets expelled by an infected person and...

