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Related Concept Videos

Sound Waves: Resonance01:14

Sound Waves: Resonance

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Resonance is produced depending on the boundary conditions imposed on a wave. Resonance can be produced in a string under tension with symmetrical boundary conditions (i.e., has a node at each end). A node is defined as a fixed point where the string does not move. The symmetrical boundary conditions result in some frequencies resonating and producing standing waves, while other frequencies interfere destructively. Sound waves can resonate in a hollow tube, and the frequencies of the sound...
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A close look at earthquakes provides evidence for the conditions appropriate for resonance, standing waves, and constructive and destructive interference. A building may vibrate for several seconds with a driving frequency matching the building's natural frequency of vibration; this produces a resonance that results in one building collapsing while the neighboring buildings do not. Often, buildings of a certain height are devastated, while other taller buildings remain intact. This...
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In the case of stringed instruments like the guitar, the elastic property that determines the speed of the sound produced is its linear mass density or the mass per unit length. This is simply called the linear density. If the string's linear density is constant along the string, then the linear density is simply the total mass divided by the total length.
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Sometimes waves do not seem to move; rather, they just vibrate in place. Unmoving waves can be seen on the surface of a glass of milk kept in a refrigerator, which is one example of standing waves. Vibrations from the refrigerator motor create waves on the milk that oscillate up and down but do not seem to move across the surface. These waves are formed or created by the superposition of two or more identical moving waves in opposite directions. The waves move through each other, with their...
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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.
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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.
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Induction of Microstreaming by Nonspherical Bubble Oscillations in an Acoustic Levitation System
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Stimulated acoustic emissions from coupled strings.

Richard S Chadwick1, Jessica S Lamb1, Daphne Manoussaki2

  • 1Section on Auditory Mechanics, NIDCD-National Institute on Deafness and Other Communication Disorders, Bethesda, MD USA.

Journal of Engineering Mathematics
|February 14, 2014
PubMed
Summary
This summary is machine-generated.

We studied wave propagation on coupled strings with decreasing stiffness. An incoming wave converts into forward and backward waves at a resonance location, with potential applications in acoustics.

Keywords:
Acoustic emissionsAsymptotic matching of inner and outer expansionsCoupled wave propagationMode conversionWKB approximation

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Area of Science:

  • Acoustics and Wave Physics
  • Mechanical Engineering
  • Applied Mathematics

Background:

  • Investigates wave propagation phenomena in coupled mechanical systems.
  • Focuses on systems with spatially varying properties, specifically decreasing stiffness.
  • Examines the behavior of transverse waves on elastically coupled taut strings.

Purpose of the Study:

  • To analyze the linear mode conversion of traveling transverse waves.
  • To understand wave behavior in a system with gradually decreasing spring stiffness.
  • To model the reflection and transmission of waves at a resonance location.

Main Methods:

  • Decomposition of the wave system into in-phase and out-of-phase modes.
  • Utilizing a local transition layer expansion matched to WKB expansion.
  • Calculating reflection and transmission coefficients for wave modes.

Main Results:

  • Identified two distinct wave modes: a transparent in-phase mode and a resonant out-of-phase mode.
  • Observed linear mode conversion where an incoming wave generates both propagating and evanescent reflected waves.
  • Quantified reflection and transmission coefficients using analytical expansion methods.

Conclusions:

  • The system exhibits complex wave behavior due to spatially varying stiffness and resonance.
  • Linear mode conversion is a key phenomenon governing wave propagation and reflection.
  • The reflected waves may serve as an analog for stimulated emissions in biological systems like the ear.