Questions tagged [vibrations]

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In counting degrees of freedom of a linear molecule, why is rotation about the axis not counted?

I was reading about the equipartition theorem and I got the following quotations from my books: A diatomic molecule like oxygen can rotate about two different axes. But rotation about the axis down ...
10k views

Why do harmonics occur when you pluck a string?

When you energise a taut string, the following resonant modes of vibration occur: Plotting on the frequency domain, you can see their corresponding frequencies: But what is the underlying physical ...
53k views

Can I compute the mass of a coin based on the sound of its fall?

Other day, I bumped my bookshelf and a coin fell down. This gave me an idea. Is it possible to compute the mass of a coin, based on the sound emitted when it falls? I think that there should be a ...
19k views

Why do tuning forks have two prongs?

I believe the purpose of a tuning fork is to produce a single pure frequency of vibration. How do two coupled vibrating prongs isolate a single frequency? Is it possible to produce the same effect ...
444 views

What is the relationship between vibration of the field and quantum fluctuation?

Consider a free field like the KG equation. I see that why $$\tilde \phi(\mathbf{p},t)$$ a momentum-dependent quantity, is an oscillator, vibrating at a frequency because when we apply the Fourier ...
24k views

Theory behind patterns formed on Chladni plates?

In this video of vibrating Chladni plates we can see small sand particles align themselves into different interesting patterns (also shown in the image below) which correspond to some particular ...
2k views

Why sound does not heat up the air?

Both thermal energy and air are propagated through vibration of particles so why sound does not heat up the air e.g loud musical instrument does not generate much heat ?
386 views

How can $F_0\cos\omega t$ change to $F_0e^{i\omega t}$ in driven oscillator equation?

I have one thing that confuses me on deriving the solution for the Linear Forced Oscillator. Suppose we have the equation as $$ma + rv + kx = F_0 \cos \omega t$$ What confuses me is when the driving ...
1k views

Vibrational anharmonic coupling and noise-induced spontaneous symmetry breaking in a hexagonal finite mechanical lattice

Happy holidays, everyone! The following is part question, part visual gallery, and part classical mechanics problem. Inspired by snow over the weekend I began simulating the vibrations of the ...
9k views

Difference between sound and heat at particle level

If heat (or thermal energy) are vibrations of particles and sound is a wave that is propagated through medium e.g vibration of air particles, what indicates if vibration of particles will be perceived ...
10k views

“Magic” Speed to Drive Over a Speed Bump: Myth or Reality?

A somewhat controversial aspect of speed bumps (sleeping policemen for those in the UK) is that they arguably cause more loss of life than they prevent by acting as a hindrance to emergency response ...
2k views

I am a high school student doing an IB Extended Essay investigation concerning the resonant frequencies of Chladni plates of differing materials and sizes. Would someone please explain the definition ...
656 views

Similarity between Schrodinger and Euler-Bernoulli equations - any possible physical meaning?

I noticed a long time ago the similarity between Schrodinger equation and Euler-Bernoulli beam equation. Namely, Euler-Bernoulli equation is equivalent to the system of Schrodinger equation for a free ...
218 views

How does a guitar work?

Here are four different possible ways: The plucked string vibrates longitudinally, vibrating the air around it. This vibrating air then causes the air inside the sound box to vibrate also, which ...
170 views

Moments of vibrating string

I have to calculate first 10 moments for vibrating string with damping, but I don't know how to do it. I read about moments and in definition they mention linear system $$x'=Ax+Bu, \qquad y=Cx$$ with ...
3k views

Extra vibrational mode in linear molecule

When calculating the number of vibrational modes for a molecule, the formulas differ for linear $(n = 3N - 5)$ and non-linear $(n = 3N - 6)$ molecules, where $n$ is number of modes and $N$ is number ...
3k views

Non-resonant but efficient frequencies

I understand that if the frequency of a driving force coincides with the natural frequency of an oscillator (say a pendulum), the rate at which energy is transferred to the same is maximized. However, ...
1k views

Is photon emission possible without electrons changing energy levels?

Does molecular vibrational transition and consequent emission of infrared radiation involve electrons changing energy level? In wikipedia, about vibronic transitions it says "Most processes leading to ...
794 views

Is molecular vibration just phonon modes for a single molecule?

I'm reading about Raman Scattering, of which a big part is measuring the energy lost to/gained from Molecular Vibrations. I wasn't totally clear on exactly what is "vibrating" in vibrational modes (is ...
27k views

Degrees of freedom in a diatomic molecule [duplicate]

We know that a monatomic compound can only have 3 degrees of freedom as we can consider it to be a point mass. However now that we consider a diatomic molecule, there are 3 degrees of freedom in ...
612 views

What is the meaning of pre-tension for a stiff membrane?

On one hand, I know that the tighter a drum head is stretched, the higher its natural frequencies. This relation is given by: $$f_{ij}=\frac{k_{ij}}{2\pi R}\sqrt{\frac{T_0}{h\rho}}$$ where $k_{ij}$ ...
2k views

Why does vibration loosen screws?

I am trying to figure out why vibrations (say, from an engine) loosen screws. It seems to me that there is evident symmetry between loosening and tightening a screw. I am wondering what breaks this ...
4k views

How do I recover the 1D wave equation from the Lagrangian?

Consider small displacements, $y(x,t)$, of an element of a string (circled in red and shown below) from equilibrium. The force balance in the vertical direction yields: +\uparrow \Sigma F: -T\sin(...
529 views

Understanding Heat

Heat or thermal energy as understood is nothing but motion of molecules of the matter. If the molecules are tightly bound (in case of solids), it is to-and-fro molecular vibrations, otherwise it is ...
138 views

Coupled ODEs that model a quad rotor

I am working on modeling the vibrations of a quad rotor. The arms that support the rotors are fixed to a center plate; that is, it is pretty much a cantilever beam with an end load. Since this is the ...
217 views

String vibration for inhomogeneous string

In case of the vibration of a homogeneous string under the boundary conditions that the string is fixed at both its ends, using fourier analysis we can show how the amplitudes of successive ...
3k views

Design of a common table fan

A few questions about the design of a common table fan, such as below. Does the round disc (silver in the image) in front of the blades serve any functional purpose? Does the metal casing around the ...
396 views

Correct definition of an 'acoustic mode'?

I am reading 'The Oxford Solid State Basics' by S.H.Simon in which on page 92 defines an acoustic mode as: ... any mode that has linear dispersion as $k\rightarrow 0$. Whilst on page 94 he defines ...
924 views

Normal modes of the 3-mass-spring system

This question might seems naive, but I'm not a physics student and got puzzled here. There are three masses placed on the plane and they form the 3 vertices of an equilateral triangle. Every two of ...
113 views

Has any scientist actually seen a $H_2O$ molecule vibrate?

Has any scientist experimentally confirmed that H2O molecules vibrate when heat energy is provided to them? Maybe by passing X-Rays through them or by some special camera...?
751 views

Actual Degree of Freedom of Diatomic Molecule

Ok, I have 2 very different values for degree of freedom(DOF) of diatomic molecules arising due to the difference in the vibrational DOF of the diatomic molecules. According to this DOF wiki page:- ...
730 views

Vibrating Objects

I'm not sure if this belongs in Engineering, but if it does, please migrate the question. What methods are used to vibrate objects extremely quickly? What are the most common?
211 views

Fourier Series Analysis [duplicate]

Can anybody explain this paragraph from the chapter " Fourier series and transform " of the book by M l Boas? "If you strike a piano key you do not get a sound wave of just one frequency . ...
429 views

Is it a linear mass-spring system?

Please look at this equation representing a mass-spring system: ${\frac {\mathrm {d} ^{2}x}{\mathrm {d} t^{2}}}+2\zeta \omega _{0}{\frac {\mathrm {d} x}{\mathrm {d} t}}+\omega _{0}^{\,2}x=F$ where ...
461 views

a Non-linear Mass-spring system with different force and vibration frequency?

I got a classic mass-spring system with zero damp ratio, having weird behaviour. The input frequency of external force is twice that of the output displacement results. While linear systems' input &...
475 views

2 Extra Degree of Freedom in Linear Triatomic Molecules?

Ok, there is a bit problem in understanding Degree of Freedom of Linear Molecules specially of Triatomic Linear Molecules. See, the DOF in general is given as $f=3N-k$. Here, N=Number of atoms in a ...
2k views

Fourier series analysis of string vibration

In case of a plucked string,the amplitudes of successive frequencies fall by 1/n^2. In case of a string which is struck so that say at x=a only the string has a velocity,say v,initially,then the ...
5k views

Can a simple pendulum be considered a simple harmonic oscillator?

Is the motion of a simple pendulum, a simple harmonic motion? It stops vibrating after sometime.
2k views

Can you hear vibrations through your bones?

If we have a source, like a speaker, but with no sound and only the vibrations, and this vibrations were transported to a surface which you can put your elbows on it and then put your hands to your ...
I derived two equations for a 2DOF harmonic oscillator system, declared state variable equations, and placed them into matrix form: $Ax' + Bx = C$. I have a Matlab script to determine the constants (\$...