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Related Concept Videos

Types of Damping01:20

Types of Damping

If the amount of damping in a system is gradually increased, the period and frequency start to become affected because damping opposes, and hence slows, the back and forth motion (the net force is smaller in both directions). If there is a very large amount of damping, the system does not even oscillate; instead, it slowly moves toward equilibrium. In brief, an overdamped system moves slowly towards equilibrium, whereas an underdamped system moves quickly to equilibrium but will oscillate about...
Damped Oscillations01:07

Damped Oscillations

In the real world, oscillations seldom follow true simple harmonic motion. A system that continues its motion indefinitely without losing its amplitude is termed undamped. However, friction of some sort usually dampens the motion, so it fades away or needs more force to continue. For example, a guitar string stops oscillating a few seconds after being plucked. Similarly, one must continually push a swing to keep a child swinging on a playground.
Although friction and other non-conservative...
Reflection of Waves01:07

Reflection of Waves

When a wave travels from one medium to another, it gets reflected at the boundary of the second medium. A common example of this is when a person yells at a distance from a cliff and hears the echo of their voice. The sound waves (longitudinal waves) traveling in the air are reflected from the bounding cliff. Similarly, flipping one end of a string whose other end is tied to a wall causes a pulse (transverse wave) to travel through the string, which gets reflected upon reaching the wall. In...
Travelling Waves01:04

Travelling Waves

A wave is a disturbance that propagates from its source, repeating itself periodically, and is typically associated with simple harmonic motion. Mechanical waves are governed by Newton's laws and require a medium to travel. A medium is a substance in which a mechanical wave propagates, and the medium produces an elastic restoring force when it is deformed.
Water waves, sound waves, and seismic waves are some examples of mechanical waves. For water waves, the wave propagation medium is water;...
Forced Oscillations01:06

Forced Oscillations

When an oscillator is forced with a periodic driving force, the motion may seem chaotic. The motions of such oscillators are known as transients. After the transients die out, the oscillator reaches a steady state, where the motion is periodic, and the displacement is determined.
Sound as Pressure Waves01:17

Sound as Pressure Waves

Sound waves, which are longitudinal waves, can be modeled as the displacement amplitude varying as a function of the spatial and temporal coordinates. As a column of the medium is displaced, its successive columns are also displaced. As the successive displacements differ relatively, a pressure difference with the surrounding pressure is created. The gauge pressure varies across the medium.
The pressure fluctuation depends on the difference in displacements between the successive points in the...

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Related Experiment Video

Updated: May 25, 2026

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
11:03

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

Forced wave motion with internal and boundary damping.

Tobias Louw, Scott Whitney, Anu Subramanian

    Journal of Applied Physics
    |January 25, 2012
    PubMed
    Summary

    This study presents a d'Alembert-based solution for wave motion with damping, simplifying transient response analysis. The method efficiently models boundary interactions and acoustic energy delivery in bioreactors.

    Area of Science:

    • Physics
    • Acoustics
    • Biomedical Engineering

    Background:

    • Investigating transient wave motion with damping is crucial for understanding physical phenomena.
    • Traditional spectral analysis is complicated by non-self-adjoint boundary conditions in wave propagation problems.
    • Modeling interface absorption and reflection effects often requires complex coupled partial differential equations (PDEs).

    Purpose of the Study:

    • To present a d'Alembert-based solution for forced wave motion with internal and boundary damping.
    • To investigate the transient response of such systems.
    • To analyze the effect of ultrasound in a bioreactor, specifically energy delivery to cultured cells.

    Main Methods:

    • Utilizing d'Alembert's method to find exact solutions for wave motion.

    More Related Videos

    Measurements of Waves in a Wind-wave Tank Under Steady and Time-varying Wind Forcing
    08:54

    Measurements of Waves in a Wind-wave Tank Under Steady and Time-varying Wind Forcing

    Published on: February 13, 2018

    Related Experiment Videos

    Last Updated: May 25, 2026

    An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
    11:03

    An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

    Published on: December 4, 2017

    Measurements of Waves in a Wind-wave Tank Under Steady and Time-varying Wind Forcing
    08:54

    Measurements of Waves in a Wind-wave Tank Under Steady and Time-varying Wind Forcing

    Published on: February 13, 2018

  • Employing dynamic boundary conditions to model interface absorption and reflection.
  • Deriving solutions for time-harmonically forced problems with internal damping.

    • Main Results:

    • Exact solutions for forced wave motion with internal and boundary damping were obtained using d'Alembert's method.
    • The dynamic boundary condition effectively models interface effects without coupled PDEs.
    • The derived solutions facilitate the analysis of acoustic field problems and ultrasound energy delivery in bioreactors.

    Conclusions:

    • d'Alembert's method provides an exact and simplified approach to solving complex wave motion problems with damping.
    • The methodology is applicable to analyzing ultrasound effects in bioreactors, optimizing energy delivery to cells.
    • This approach offers a concise framework for acoustic field analysis in various scientific and engineering applications.