Questions tagged [vibrations]
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The definitions of coherent phonons and acoustic phonons
I found that the definition of coherent phonon: A femtosecond laser pulse can initiate collective, in-phase atomic motions in solids called coherent phonons.
My question is: what is the difference ...
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Can someone please explain how is the setup stated below apparently causing amplitude resonance in spite of different frequencies?
Suppose I have a pendulum such that its natural frequency is $2 Hz$.
I release it from One extreme by striking it with a tuning fork of frequency $1 Hz$. Now in $0.5s$, the pendulum will undergo 1 ...
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Are Harmonic or Subharmonic resonance the only outcomes for a system with applied vibrations?
I'm working on performing a linear stability analysis on a system with fluid undergoing applied vibrations. Now, usually these systems are analyzed with no fluid velocity. Under these conditions, it ...
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Phonon eigenfrequencies under time reversal
In G. P. Srivastava's "The Physics of Phonons", 1e., the ansatz which solves Newton's second law in the harmonic approximation is taken to be
$$
u_\alpha(\ell b;t)
=\frac{1}{\sqrt{m_b}}\...
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How to interpret huge number of phonons?
In my condensed matter class we have seen how to treat the problem of vibration in a lattice in quantum mechanics. After heavy calculation we derive that the number of phonons with a given crystal ...
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What is happening to the air pressure in an extremely high-intensity low-frequency sound wave e.g. 30 Hz at 100 dB?
I'm doing research on low-frequency sound in music and one text states 'High-sound pressure levels condense air – noticeably thickening it, making it feel heavier.'
Is this true and what does that ...
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Anharmonic effects in crystals, help with intuition
I've been reading a bit about how it is necessary to consider anharmonic effects in crystals if one wants to properly understand things like thermal expansion etc. So for example here:
So the cubic ...
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Modes of vibration
I've been thinking that 'modes of vibration' refers to the frequencies which produce standing waves in a system. But now I'm confused, because ChatGPT gave me the below response for my question.
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Magnetic field changes induced by vibrating electric guitar string
Here is a picture (from a paper by Feinberg and Yang in the Journal of the Acoustical Society of America) of an electric guitar string vibrating (mostly in the $y$ dimension) near a permanent magnet.
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Calculating vibrational mode coefficients of a drum for an arbitrary excitation
I am interested in the modes of a rectangular drum of size WxL that is fixed on 4 edges. The differential equation that governs the vibrations of a 2D membrane is $\nabla^2 \phi - \frac{1}{c^2}\frac{\...
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How to find the amplitude of the membrane of the speaker if the the input voltage is known?
Can anyone tell me what are the relevant pieces of information that are required to find the amplitude of a speaker membrane for a particular input ac signal frequency and voltage amplitude? Could you ...
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Do vibrational frequencies produced from sound pass through your entire body? from one side to another? [closed]
when there is a noise by me, i feel the vibration on my skin from the direction it’s coming, it moves into my body. a wall of what sound would feel like passing through me. i perceive it as container ...
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Fourier transform for diagonalizing the Hamiltonian of lattice
I am reading the first chapter of "Statistical Theory of Fields" by Kardar. There he discussed the idea of phonons.
Consider an ideal lattice at zero temperature with lattice vectors $\vec q^...
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Sum of incident and reflected waves being the transmitted waves amplitude
Suppose we have an incident wave $\psi_i$ heading towards an interface, then when it reaches the interface it is split into a reflected and a transmitted wave:
$$ \psi_i \to \psi_r + \psi_t $$
Why ...
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Coupled pendulum question about equations of motion [closed]
I am working on problem number 2.3 of the Franklin, Powell, Naemi book Feedback Control of Dynamic Systems. The problem uses the simple coupled pendulum system below, where the two pendulum masses are ...
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Why do vibration MEMS gyroscopes need two oscillating modes?
Everywhere I look, I see that MEMS gyroscopes need to have two modes, that are orthogonal in direction. However, that puts a lot of significance to the detuning of these modes, and calls for highly ...
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Linear Triatomic Molecule Bending Vibration Modes
In the Oscillations chapter of Goldstein Poole and Safko (3E, Ch 6), there is a discussion of the symmetric linear triatomic molecule (classical model, obviously). Initially, the 3 longitudinal modes ...
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What exactly are sympathetic vibrations?
On every source and in every example, it seems that sympathetic vibrations are quite directly linked to or are the same as resonance.
The classic example of sympathetic vibrations is of two similar ...
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How to test resonance frequency of spring using sound?
I've done experiment with spring and mass to determine the natural frequencies of 4 springs. The first experiment went well but I had some problem when I want to test the resonant frequency. I'll ...
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How would you experimentally determine the damping coefficient of a system?
We have a suspended beam that we need to determine the natural frequency, and more importantly the damping, of. To avoid resonance.
The geometry of the beam is a little too complex to rely on theory ...
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Does vibrational energy transfer to translational energy when an excited $\rm CO_2$ molecule collides with an $\rm N_2$ or $\rm O_2$ molecule?
My understanding is that when a $\rm CO_2$ molecule absorbs a photon of heat in the atmosphere after some time it simply re-emits that photon in a random direction. If that photon makes it back to its ...
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Exciton-phonon coupling Hamiltonian
I'm reading this article about coherent exciton transport in photosynthetic light harvesting and the role of quantized vibrations. Along the way, I came across a section where the article claimed the ...
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"Spherical wave" in a 2D square lattice of masses and springs
Assume a 2D square array of masses with mass $m$ connected by springs with constant $\kappa$. Then the equation of motion for small perturbations in the plane of the array to the mass at $(l,n)$ is
$$
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Birefringince in 2D array of masses and springs
Assume a 2D square array of masses with mass $m$ connected by springs with constant $\kappa$. Then the equation of motion for small perturbations in the plane of the array to the mass at $(l,n)$ is
$$
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Vibrational spectroscopy energy spectrum
I have a question regarding vibrational spectroscopy. In vibrational spectroscopy we are describing the vibration of molecules with the Morse potential which gives us stationary wavefunctions that ...
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Why is an ultrasonic transducer able to send energy into a tank without an opposing surface?
The diagram shows an ultrasonic transducer stuck to the bottom of an ultrasonic cleaning tank full of water/detergent. It's not supported at the opposing end - just hanging off the bottom of the tank. ...
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Source term and potential term in wave equation
I have often seen the wave equation as:
$\Box \psi(x_1,x_2,x_3) + V(x_1,x_2,x_3)\psi(x_1,x_2,x_3) = S$; where $V$ represents the potential term ans $S$ represents the source term.
I want to know that ...
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Calculation of normal frequencies of a normal mode
In the Classical mechanics book by Goldstein, it is stated that if one wants to find the normal frequencies of a system, $\omega$ then the following equation has to be solved:
$\left|\hat{V}-\omega^2\...
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Underdamped and overdamped molecular vibrations
I am reading about the interactions between excitons and phonons in this article, and I came across the following equation for the underdamped component of the spectral density of the vibrational bath:...
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Energy of polyatomic molecular vibrations
I understand that the energies of a simple diatomic molecular vibration are equal to $E_n=(n+\frac12)\hbar\omega$, and I also know the accompanying eigenfunctions for these energies. I have also heard ...
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Seeking resources on mass-sensitive vibration modes for structures
I recently came across the topic of mass-sensitive vibration modes for structures in a research paper, but I have not been able to find many other resources on this topic.
I am particularly interested ...
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Energy of molecular vibrations
I have just read that the energy of a molecular vibration with frequency $\omega$ has eigenvalues of $(n+\frac12)\hbar\omega$, where $n$ is the quantum number. However, this equation really surprises ...
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Eliminating sound vibrations by using destructive interference for sound waves
Can you eliminate sound vibration (when either it is audible sound, ultrasound or infrasound) by creating a destructive interference, but when both sources are in opposite sides?
Say, you have one ...
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What do we mean by 'resonance frequency' of a system?
Whenever we talk about oscillations, we generally take the term 'resonant frequency' for granted, but I don't understand what this frequency depends on.
For example, if we talk about a freely ...
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FFT plot not aligning with lower natural frequencies
I have a cantilever beam with gapped springs on top and bottom and an impulse is given at the free end initially.
I modelled it using finite element method with 30 elements.
The beam then oscillates ...
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Multiple Pendulums and Resonance
Set up with multiple pendulums suspended from a connecting string. Pendulums 1 and 4 have the same lengths and hence, the same natural frequencies. Others(pendulums 2, 3 and 5) are of varying ...
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Vibrating membrane tension per unit length
I have been working on the problem of a vibrating membrane, with all the assumptions to make it ideal, but I still can't figure out why the tension per unit length multiply like that:
if $T$ is the ...
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How is maximum amplitude of resonance achieved?
Lets take a simplest case of a narrowly tuned system and the outside force exactly at the natural frequency of it. The first pulse will go through, bounce back somewhat weaker and get reinforced by ...
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What are the best intuitive books to learn in-depth about waves and oscillations? [duplicate]
I was looking for a book/s that does not necessarily use a textbook-esque approach (e.g just providing definitions, equations, and examples) but dives deeply into the philosophy behind their mechanism,...
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How to find Shear Force and Bending Moment in Finite Element Method for a cantilever beam with many elements
I have a cantilever beam with lots of elements. I am trying to find the sheer force and bending moment diagrams of the beam.
EVERY SINGLE TUTORIAL AND EXAMPLE I SAW ONLINE SHOWS HOW TO DO IT FOR A ...
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Motorcycle handle Bar vibration & Bar End Weights
Pic 1 is a normal motorcycle bar end weights.
My question, if I replace the bar end weights with a long threaded rod (M8x150) and the thread rod is inserted inside the handle bar(pic 2), will it ...
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Transverse Vibrations of a Cantilever beam. Why does the % change in nth natural frequency increases with n in this case?
This is the problem in detail
I have a cantilever beam.
Now I am making it stand upright and adding water for different heights of SUBMERGENCE
I am doing this by adding an ADDED MASS term from the ...
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Parameters which affect the transmission strength of a signal (vibrations) in a solid?
I'm working on a pair of devices - a signal injector and a matched detector for vibrations in solids. My background is not in acoustics, so I'm looking for pointers on what are the parameters that ...
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Condition for true periodicity
In Vibrations and Waves, French writes that
The condition for any sort of true periodicity in the combined motion is that the period of the component motions be commensurable- i.e., there exist two ...
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Is vibratory motion in straight line also pure translatory motion?
I think pure translatory motion is defined as change in position of the object such that the velocity of each particle of the object is parallel and in the same direction to each other and is of the ...
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Phonon modes and atom vibrations vs temperature
My understanding is that number of phonon modes depends on the number of atoms in a system and will be gradually populated with increasing temperature until Debye temperature. At the same time, atoms ...
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Choosing a Complex Trial Solution for a Forced Vibration Problem and Expressing The Driving Force in Complex Terms
When solving forced vibration problems I would always choose a trial solution for the particular (stead-state) case in the form $x(t) = A \cos{\omega t} + B \sin{\omega t} $, but reading some books I ...
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How do you Determine the Fastest Vibrational Mode of a Crystal?
I understand that a crystal's vibrational modes are Phonons and have a minimum wavelength that is limited by twice the equilibrium separation between neighbouring atoms. But I don't understand how you ...
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How to know if the vibration system requires one degree of freedom or two? and how to pick the right coordinate to describe the movement?
I want to know a trick that helps me understand oscillatory systems and how to pick the correct general coordinates that describe the movement, I tried everything but I still can't get the solution ...
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String vibration under periodic boundry conditions
I wish to known which are the vibration modes (in case that they exist) of an string vibrating under periodical boundary conditions (PBC).
The question is related to molecular dynamics simulations of ...
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