Harmonics Definition and 264 Threads

Homework Statement I want to understand spherical harmonics. I want to really grok them deeply. I want to be able to visualize them and understand them. I'm the sort who can't take anything on faith, especially where quantum mechanics is concerned. So I want to understand angular...

Hi folks, I'm looking for a derivation of the following statement (formula 76) http://img845.imageshack.us/img845/1550/screenshot4op.png Do you know any reference, where I can find a bit more detailed description? I reckon, you can find it in Jackson's electrodynamic book, but I couldn't find...

Is the second harmonic produced by middle c on the organ the same as the C note in the following octave? just a little confusion

Homework Statement A person hums into the top of a well and finds that standing waves are established at frequencies of 42, 70 and 98 Hz. The frequency of 42 Hz is not necessarily the fundamental frequency. The speed of sound is 343m/s. How deep is the well? Homework Equations just harmonic...

ok so i have a major confusion and its really getting to me. So from what i understand of harmonics, the length of the medium is always fixed and only the frequency changes. Is this right? Then why, on organ pipes for example.Assume open open configuration. Say I play a middle tone note C...

I am learning to play guitar now, I am wondering why guitar strings always give the same sound (pitch). In my opinion, it is because it is always the fundamental, but why there is never presence of harmonics during playing? Also there is a technique in guitar playing called HARM. You just put...

Homework Statement The fundamental frequency of a piano string with mass of 7g and length 80cm is 261.63Hz. What is the tension on the string? If we coil the string duplicating its density(without changing length I presume), what is its new fundamental frequency? If 16000Hz is the highest...

Homework Statement A glass tube with one end open and the other closed is used in a resonance experiment to determine the speed of sound. A tuning fork of frequency 427 Hz is used and resonance is observed for air column lengths equal to 17.4 cm and 55.0 cm. (a) What speed of sound does this...

I have a question which I would like to know the answer to, I posted it before but don't think I was understood correctly, hopefully I can make myself clearer this time. Every physical object in this universe has a natural or resonant frequency from an atom to a planet. Attached is an image of...

Hi, this may seem like something I should ask in the math forums but, as I came into this problem in atomic physics I'm confident that this is a question more appropriate here than in the math forums. So far I've been only able to find the common integral of a product of three spherical...

Homework Statement I have to construct 3, 3X3 matrices for Lz, Lx, Ly for the spherical harmonics Y(l,m) given l=1 and m = 1,0,-1 So I can determine the relevant harmonics for these values of l and m. I act with Lz on Y to get L Y(1,0) = 0 L Y(1,1) = hbar Y(1,1) L Y(1,-1) =...

I thought I would try to discuss this here since there seems to be a large misunderstanding in automotive forums and I want to learn the reality, not someone's theory. basically, I have a car here in which we removed one of the many mufflers. Piping is constructed as 2-1-2. It converges to...

Homework Statement The function cos(theta)*cos(phi) in spherical coordinates cannot be expanded to a series of spherical harmonics. Explain why. Homework Equations As far as I can recall, the spherical harmonics are a complete set over a sphere, meaning every function which is SI over a...

What is the relationship between harmonics and wave amplitude in a resonant object? Lets say we have an object which has a natural resonant frequency of 50hz. we connect that object to a signal generator set at 50hz and note the amplitude of the oscillations the object. Next we go up one...

Hi, I need expand a spherical function(real function not a complex function) in terms of spherical harmonics. Expansion coefficients are complex numbers. If i need to observe physics quantities that are represented by the spherical harmonics coefficients which part should i look at- real part...

Due to non-linearity of magnetic core of large transformer, Which is excited by pure sinusoidal voltage source, the exciting current isn't perfectly sinusoidal. It can be thought to be composed of pure sinusoidal plus mainly 3rd harmonic component. But does this current flows in the primary...

Homework Statement A vertical, 1.13m length of 18-gauge (diameter of 1.024mm) copper wire has a 200.0N ball hanging from it. What is the wavelength of the third harmonic for this wire? A 1000- ball now replaces the original ball. What is the change in the wavelength of the third harmonic...

Homework Statement Two ukulele strings, of equal length and mass are tuned so that the first string, when it vibrates at twice its fundamental frequency, has the same frequency as the second string when it vibrates at three times its fundamental frequency. The tension of the first string is...

Low Cost "Harmonics Generator" Hi, Thanks in advance. I noticed how good is this forum so I decided to share my thoughts with you about the following. If possible, I need some ideas from you guys to build a low cost circuit to generate only 2nd an 3rd harmonics for a 120v 60hz sinewave input...

Greetings, I’m looking at the output of an electronic 3-phase meter. I have 2 “snapshots” from the meter. In one snapshot I can make sense of most of the data presented. The output gives me Va, Vb, Vc, Ia, Ib, Ic, and their angles, a single power factor, watts, VA, and VAR. When I...

If I look at the Fourier transform of the square wave signal, the peaks are at the odd multiples. In the device that I am working on, I would expect the interference at the odd harmonics of the center frequency. But I see the interference at even harmonics. When is this possible? (Only if...

Homework Statement a) Find the potential of an axial quadrupole: point charges q, -2q, and q placed on the z-axis at distances L, 0, and -L from the origin. b) Find the potential only at distances r>>L. c) Show that this potential is proportional to one of the zonal harmonics.Homework...

As an example of a standing wave we have a musical tone, which is a combination of a fundamental pitch and a series of harmonics. Is there anything to suggest that additional harmonics don't continue up far beyond the range of hearing, perhaps even approaching infinity? Or is there some point...

u(r,\theta,\phi)=R(r) Y(\theta,\phi) Where Y is the spherical harmonics \frac{\partial^2 Y}{\partial \theta^2} + cot\theta \frac{\partial Y}{\partial \theta} + csc^2 \frac{\partial^2 Y}{\partial \phi^2} + \mu Y = 0 The book said this equation has nontrivial solutions when \mu =...

what is the difference between ripple and harmonics?? particularly please explain harmonics... how it actually is harmfull .. and what is the reason of its origin?

Homework Statement When you have an open-closed tube, I was taught in high school that when using the equation λ = 4L/m, m = 1, 3, 5, 7, ... where m = 1 corresponds to the fundamental mode. I was taught that m = 1 is the 1st harmonic, m = 3 is the 3rd harmonic, etc. But my physics...

Homework Statement One end of a horizontal string is tied to a wall, and the other end is tied to an object with weight W that hangs over a pulley to hold the string taut. The object is large enough that the string never moves at the pulley. Under these conditions, the string vibrates with...

When solving the time-independent Schrodinger equation for a spherically symmetric potential, using the separation of variables, we find that solutions of the form \psi =R(r)Y_l^m(\theta ,\phi) where the Y_l^m are the spherical harmonics. We apply this to the (idealized) electron in a Hydrogen...

Why do strings, etc vibrate in harmonics? Is it a characteristic of all waves, a consequence of the way energy propagates along a wave? If so, how?

This isn't actually a homework/coursework question, but rather a need to clarify a discepancy between my lecturer's notes and a textbook. My lecturer's notes state that for an "organ" pipe, closed at one end, the 1st harmonic frequency will be 4L. For the 2nd harmonic the frequency will be...

Homework Statement The complete wavefunction for a particular state an atom, is Si(r,theta,phi)=Ne^(-Zr/a_0)(Z/a_0)^3/2sqrt(1/4pi). What is the eigenvalue Lz for this state?Homework Equations see above The Attempt at a Solution This is the last one that I'm having trouble with. I have no...

Hello everyone, I desperately need some help in understanding spherical harmonics and I would be really grateful if someone could help me understand them intuitively. So, as I understand SH are another way to represent a function as a linear combination of some basis functions but the...

Hello, I had posted this in the 'General math' section and did not get any response. Maybe it belongs in this group as it is more related to function decomposition. I hope I am not breaking any forum rules and it is not my intention to cross-post. Just reading an essay about spherical...

Let's define operator P: P \phi(\vec{r})=\phi(-\vec{r}) Does anyone know simple and elegant prove that P|lm\rangle = (-1)^l |lm\rangle (|lm\rangle is spherical harmonic).

Homework Statement I am trying to calculate the angular momenta for \psi(x,y,z) = A(ar^2 + bz^2) A is given as a constant. Homework Equations The Attempt at a Solution I know that z=r\sqrt{4\pi/3} * Y_0^1 What I have so far is:- \psi(x,y,z) = r^2Aa +...

I cannot figure this out! Please help! Q: A Spaceship lands on a new planet. The crew decides to measure the speed of sound by blowing across one end of a tube. The tube is 50cm long, and the crew finds one resonant frequency at 1620Hz and the next resonant frequency at 1980Hz. What is the...

Homework Statement What is the result of raising momentum ladder operator (L+) acting on spherical harmonics Y04 (\theta,\phi) Homework Equations The Attempt at a Solution I was expecting Y14 (\theta,\phi) I applied L+ on Y04 (\theta,\phi) and ended up with Y14...

Lets consider the equation: \nabla^2 f=0 I know that in spherical coordinates this equation may be decomposed into two equations, first which depends only on r, and the second one which has the form of spherical harmonics equation except that the l(l+1) is an arbitrary constant, let's say C...

Why does half a wave length and not a full wave length constitute the first harmonic? v=\lambdaf because a standing waves can be made with two half waves traveling in opposite directions?

I don't understand how to get n... if that doesn't make sense i can explain more... I have the length and velocity... from there i just don't understand what n even is or means...

Homework Statement Find the speherical harmonics (Y_1)^1, (Y_1)^0, (Y_1)^-1 as functions of the polar angles \theta and \psi and as functions of the cartesian coordinates x, y , and z. Homework Equations \(phi_l)^l= sin^l(\theta)*e^il\psi L_\(phi_l)^l=(d/(d\theta))*\phi_l^l-l...

Homework Statement A small town’s noon hour whistle is an air column 0.750 m long and closed at one end. Find the fundamental frequency and the next harmonic produced by this whistle when the speed of sound in air is 342 m/s. Homework Equations f= v/λ, The Attempt at a Solution...

Hi all, just an very elementary question, arising from the first study of generating harmonic solutions. How to get the gradient twice for 1/r in spherical coordinates?

Hello, everyone! I'm working on parametrizing a magnetic field using spherical harmonics. The equations Yc n,m (theta, phi) = (R/R0)^n * Pn,m(cos(theta)) * cos(m*phi) Ys n,m (theta, phi) = (R/R0)^n * Pn,m(cos(theta)) * sin(m*phi) where Pn,m is a Legendre polynomial where n is degree and m...

Homework Statement I am trying to find the equation for lambda four for mechanical harmonics. Homework Equations I know that lambda1=2L, lambda2=L, lambda3=2L/3, but neither google nor my textbook have the equation for lambda4! The Attempt at a Solution I have searched my physics...

I am trying to write the term "Sin^2 theta * Sin 2 phi" in terms of spherical Harmonics (they form a combination of Y(2,-2) and Y(2,2)) but the term I get contains the imaginary number 'i'. Am I doing something wrong.. In fact this term is a part of a Hamiltonian and when I get the eigenvalues I...

Hi all, :smile: My understanding of harmonics in general is quite sketchy and as a result my query might appear a bit lulu! :rolleyes: I tried the net but could not get suitable info on the same. This is what I'm looking at; Assume a battery hooked up to an inverter (1 phase or 3 phase...

So, I was reading about the quantum http://en.wikipedia.org/wiki/Rigid_rotor" and apparently its solutions are the so-called spherical harmonic functions, which are the solution to the angular portion of Laplace's equation. The way I see it, the rigid rotor Schroedinger equation is not the...

http://buyanik.wordpress.com/2009/05/02/laplacian-in-spherical-coordinates/"

Homework Statement Show: \psi_1=N x e^{-\frac{x^2}{\sigma}} is an eigenfunction of the total energy operator(H). Homework Equations psi=N x exp[-x^2/K]The Attempt at a Solution I plugged in the above to the Schrodinger Equation-time indep. for Harmonic oscillator but I keep getting an x^2...