Helmholtz Definition and 179 Threads

Hi, Consider P = \boldsymbol{\nabla} f +\boldsymbol{\nabla}\times \bold{A} where f and A are scalar and vector potentials, respectively, and P is strictly positive and well behaved, and only nonzero in a domain \mathcal{D}. I want to find how the magnitude of \int \boldsymbol{\nabla} f dV...

Homework Statement I'm interested in the solution of an equation given below. (It's not a homework/coursework question, but can be stated in a similar style, so I thought it best to post here.) Homework Equations A \nabla^2 f(x)-Bf(x)+C \exp(-2x^2/D^2)=0 where A,B,C,D are...

Homework Statement I have a bit of a problem in class. I am attempting to do an assignment on sound in relation to a guitar. For this I need to explain how the guitar is a highly energetic intrument. I do not know if looking at is like a helmholtz resonator is a waste of my time or not but I'm...

Homework Statement Show that the Green's function for the two-dimensional Helmholtz equation, ∇2 G + k2 G = δ(x) with the boundary conditions of an outgoing wave at infinity, is a Hankel function of the first kind. Here, x is over 2d. Homework Equations The eigenvalue...

I'm currently learning thermodynamics from Schroeder's "An Intoduction to Thermal Physics". He explains that in an environment of constant temperature, the system can extract heat from the environment for free when we create a system, and the Helmholtz free energy is that additional work needed...

Is defined as F = U - TS and it is the energy needed to create a system minus the heat it can get for free. But why is the heat that it can get for free given by: Q = TS I know the thermodynamic relation: S = Q/T So in that way I understand it. But how do you know, that the system will be...

I'm having some trouble understanding this concept. Why is it that you sometimes can get heat for free from the environment? Like suppose you have a system, on which you make an energyconsuming proces which creates entropy. Then you subtract TΔS because apparently heat can enter when the entropy...

I'm having some trouble understanding this concept. Why is it that you sometimes can get heat for free from the environment? Like suppose you have a system, on which you make an energyconsuming proces which creates entropy. Then you subtract TΔS because apparently heat can enter when the entropy...

Homework Statement it is stated in wikipedia http://en.wikipedia.org/wiki/Helmholtz_equation that "Here, G is the Green's function of this equation, that is, the solution to the inhomogeneous Helmholtz equation with ƒ equaling the Dirac delta function, so G satisfies [del^2 +...

First, I find the term "resonance" and its relatives to be used quite loosely. What is the actual definition according to physics/acoustics. An example of its used: The port of a Helmholtz Resonator resonates at the system's resonant frequency. The port itself is not that thing resonating...

Homework Statement Arfken & Weber 9.7.2 - Show that \frac{exp(ik|r_{1}-r_{2}|)}{4\pi |r_{1}-r_{2}|} satisfies the two appropriate criteria and therefore is a Green's function for the Helmholtz Equation. Homework Equations The Helmholtz operator is given by \nabla ^{2}A+k^{2}A...

Homework Statement The Helmholtz free energy of a certain system is given by F(T,V) = -\frac{VT^2}{3}. Calculate the energy U(S,V) with a Legendre transformation. Homework Equations F = U - TS S = -\left(\frac{\partial F}{\partial T}\right)_V The Attempt at a Solution We...

Homework Statement It is actually not homework, but I found it is cool to solve it in Scilab, and I think that it is more proper to ask it here write the codes for (please read the picture)Homework EquationsThe Attempt at a Solution u=1.256637061*10^-6 N=320 R=0.136/2 a=2*R Z= [-0.17 -0.15...

Hi guys, This may be a daft question (or set of questions), but I just want to bounce a few ideas off the wall once I understand some simple issues. Can anyone tell me why if you pass a current through a wire in a magnetic field, the wire will move perpendicular to the both the current...

For a thermodynamic process, what equations would be used to find the change in Gibbs and Helmholtz free energy when: a.)The process is adiabatic b.)The process is isothermic c.)The process is at constant volume d.)The process is at constant pressure I know ΔG=ΔH-TΔS and ΔA=ΔU-TΔS but do...

Homework Statement Find the Green's Function for the Helmholtz Eqn in the cube 0≤x,y,z≤L by solving the equation: \nabla 2 u+k 2 u=δ(x-x') with u=0 on the surface of the cube This is problem 9-4 in Mathews and Walker Mathematical Methods of Physics Homework Equations Sines, they have the...

If I was only considering the "elliptical arc" as 1/6 of a circle and all I was concerned with was the radial and angular dependencies (w.r.t.) and two sinusoidal sources acting in unison as the forcing term which is actually 2 sin(60t), how would this wave equation be set up and what would be...

Helmholtz resonator? Intake manifold design Hi guys, I'm doing a bit of research into engine intake manifolds. The information I've found so far looks staright forward, but it's given out by turners and cottage industry designers, rather than engineers or physicists, so it's basic. I...

Hello PFs, I need to build some Helmholtz coils, and I was wondering if anybody here had suggestions on what to make the actual rims that hold the wire in a coil are generally made out of? So far its been suggested that I use bicycle rims, but even that creates a question--aluminum or steel...

PDE : Can not solve Helmholtz equation (This is not a homework. I doing my research on numerical boundary integral. I need the analytical solution to compare the results with my computer program. I try to solve this equation, but it not success. I need urgent help.) I working on anti-plane...

How to get U(r) and W(r), why are them defined out of nowhere, is that the standard structure of that kind of functions ( what kind of functions are them??) ? T.Y

Homework Statement Hi there. I have this problem which I'm trying to solve. Its from callen, it says: Two ideal van der Walls fluids are contained in a cylinder, sparated by an internal moveable piston. There is one mole of each fluid, and the two fluids have the same values of the van der...

Hi I'm suppose to find the direction of the magnetic field and the current in the diagram below and I was just wondering if I did this correctly. (red is magnetic field and blue is the current) Diagram: http://i324.photobucket.com/albums/k327/ProtoGirlEXE/100_0702.jpg And I have a few...

Hi, I'm building a pair of helmholtz coils to do a variety of magnetism-related experiments. I've borrowed an old Avo Douglas coil winder and plan to do a couple of thousand turns on two sections of 50mm or 60mm diameter pipe. Some nylon threaded rod will pass through the middle of each coil...

Homework Statement Show that \epsilon(r)=\frac{A}{r}e^{ikr} is a solution to \nabla^{2}\epsilon(r)+k^{2}\epsilon(r)=0 Homework Equations The Attempt at a Solution Is \nabla^{2} in this case equal to \frac{\partial^2}{\partial r^2} or \frac{\partial^2}{\partial x^2}+\frac{\partial^2}{\partial...

Hello physics enthusiasts! I was looking for resources, and stumbled upon these awesome forums. I am looking for how to solve the helmholtz equation / wave equation on a figure 8 type shape. I wanted to find the resonant frequencies of a classical guitar. Would this work? I am considering...

Homework Statement Let H(r) = x^{2}yi + y^{2}zj + z^{2}xk. Find an irrotational function F(r) and a solenoidal function G(r) such that H(r) = F(r) + G(r) Homework Equations From Helmholtz's theorem, any vector field H can be expressed as: H = -\nabla\Psi + \nablaxA So then: F...

Homework Statement Let H(r) = x^{2}yi + y^{2}zj + z^{2}xk. Find an irrotational function F(r) and a solenoidal function G(r) such that H(r) = F(r) + G(r) Homework Equations From Helmholtz's theorem, any vector field H can be expressed as: H = -\nabla\Psi + \nablaxA So then: F =...

Homework Statement We have 2 circular loops, each of radius R with current I in same direction. This is called a Helmholtz coil. The loop axes are along the z axis and the centers are at z=+/-s/2. Find the magnetic field along the z axis between the 2 loops. Homework Equations...

Hi, I'm doing a project that involves the use of Helmholtz coils. We have coils and can calculate the magnetic field produced using the standard equation and taking everything into consideration. I know we can boost the magnetic field strength of the coils by introducing and iron...

When it comes to thermal/statistical mechanics, I'm a little retarded... so bear with me please. I've used the helmholtz free energy (F) dozens of times, almost as many times as I've heard and read that F is a measure of the 'useful work attainable from a closed thermodynamic system,' at...

I have an airbox on a motorbike and want to find its frequency. I have two formulas: f = w / 2pi = 160 sqrt( 116.5 A / VL ) and f = ((343m/s) / 2PI) * SQRT( A / VL) A = Area of intake neck = 5.67cm^2 or 5.67x10^-4m^2 V = Volume of airbox = 2500cc or 2.5x10^-3m^3 L =...

Homework Statement The diagram illustrates a Helmholtz coil, consisting of two identical circular coils of wire, each one having N loops and carrying the same current I. The radius of each coil is R, and the two coils are R meters apart. (a) What are the direction and strength of the...

Homework Statement To state the differential form of the Helmholtz thermodynamic potential and derive the corresponding Maxwell's relation. Homework Equations Stated within the solution attempt. The Attempt at a Solution Helmholtz function: F = U - TS Calculating the...

I have to show that a generic vector can be decomposed into an irrotational and solenoidal component: V(r) = -Grad[phi(r)] + Curl[A(r)] I'm not sure how to start. Do I need to take the curl or div of V and use a vector identity? Any help would be greatly appreciated!

Hello all, This is to do with forced longitudinal vibration of a rod (bar). It's basically a problem to do with the linearised plane wave equation (1d). The rod is fixed firmly at one end, and excited at the other by a harmonic force. The wave equation (with constant rho/E instead of...

Homework Statement In 2D: (del2 + k2) u(r,theta) = 0 with b.c u(R,theta) = f(theta) Starting from the general solution (by separation of variables) show that the solution can be rewritten as: \int K(r,theta,theta')*f(theta') dtheta' from 0 to 2*Pi Homework Equations The general solution is...

hi everyone, I am dealing with a numerical method to solve the Helmholtz equation. As far as I know it is a second order elliptic PDE. I would like to know, if the Maximum Principle (aka Boundary Maximum Principle) holds for the Helmholtz eq., or where can I find explicit literature about it...

Dear Sirs, I was asked to design a Helmholtz coil. Being an electronic engineer, I can design electronic circuits but I have no idea about designing Helmholtz coils. Can you help me by suggesting a paper or article that describes a straightforward, step-by-step method for designing these...

I'm seeking help in understanding Kirchoff-Helmholtz Integral. Actually what i am facing the problem here is, i don't understand certain things about Green's 2nd identity which stated that two scalar function can be interchanged, and forming the force F = \phi\nabla\varphi -...

Hi, I have been trying to find the (causal) Green's function of \frac{\partial^2 \phi}{\partial t^2} + \frac{\partial^2 \phi}{\partial x^2} + \frac{\partial^2 \phi}{\partial y^2} + m^2 \phi = 0. What would be a good way to approach this? I have initial values for t=0, so I use...

Hi guys, We all know that Helmholtz free energy, Gibbs free energy and Enthalpy are defined by Legendre transformation. For Enthalpy H=E+PV, I can understand it as the energy required to "displace the atmosphere" plus "creating the internal energy of system". What about Gibb free energy...

Homework Statement The Helmholtz free energy is written as: dA=-SdT-pdV-VMdH when an incompressible liquid is placed in a magnetic field H. Thus, the free energy can be written as since -pdV=0: dA=-SdT-VMdH The two heat capacities can be defined as: C_H = T (dS/dT)_H and C_M = T...

hi guys.. I'm trying desperately to solve the following Helmholtz equation: *(all parameters are known) \frac{\partial^2 E_z}{\partial x^2}+ \frac{\partial^2 E_z}{\partial y^2} +j\omega\sigma E_z=0 (Ez is a scalar of course) in the boundaries -inf<x<inf, -inf<y<0 with the...

Homework Statement Show that the most probable energy minimises the Helmholtz free energy. Homework Equations F=E-TS(E) where S(E) is the entropy of te system of given energy E. The Attempt at a Solution Not sure how you would 'show' is ? P(E) = 1/Z *weight funciton*exp(-beta E)

I'm trying to find a divergenceless vector field based on its curl, and discovered that I could use a http://en.wikipedia.org/wiki/Helmholtz_decomposition" , and the article I found on this didn't make much sense to me. First, can someone confirm that the dimension referred to in the...

I'm trying to find a divergenceless vector field based on its curl, and discovered that I could use a http://en.wikipedia.org/wiki/Helmholtz_decomposition" , and the article I found on this didn't make much sense to me. First, can someone confirm that the dimension referred to in the...

Homework Statement Explain why the formula (dF/dV)=-P , where T and N are constant variables , makes intuitive sense, by discussing graphs of F vs. V with different slopes. Homework Equations The Attempt at a Solution dF=SdT-PdV+mu*dN dT and DN are zero since T and N are...

Hello! I'm in a search for information on the topic to devise a strategy of solving H. equation in N dimensions with Dirichlet - von Neumann type of boundary conditions. I'm assured that problem can be solved in closed form. As far as I can see, boundary conditions in any number of...

Homework Statement Use the definitions of Helmholtz free energy, F, and Gibbs free energy, H, together with the thermodynamic identity, to show that S = -(\frac{\partial F}{\partial T})_V and S = -(\frac{\partial F}{\partial T})_P Then use those definitions again, and the...