Harmonics Definition and 264 Threads

I found an interesting thing when trying to derive the spherical harmonics of QM by doing what I describe below. I would like to know whether this can be considered a valid derivation or it was just a coincidence getting the correct result at the end. Starting making a Fundamental Assumption...

How does one arrive at the equation $$\bigg( (1-z^2) \frac{d^2}{dz^2} - 2z \frac{d}{dz} + l(l+1) - \frac{m^2}{1-z^2} \bigg) P(z) = 0$$ Solving this equation for ##P(z)## is one step in deriving the spherical harmonics "##Y^{m}{}_{l}(\theta, \phi)##". The problem is that the book I'm following...

Say you were building a full-wave rectifier. How many simple ways (if any) are there to reduce the THD on the source caused by using a full-bridge rectifier load? Also, If you used a low pass filter and then an isolation TX (or the other way around?), how much would that help to this end (if at...

I'm currently reading class notes from an introductory waves course, written by the professor himself. I'm stuck in the Fourier analysis part, because he gives the formulas for the nth mode amplitude of a standing wave with fixed ends and then states some properties which I can't really make...

What effect do harmonics have on wye-wye transformers with neutral grounded? What about not grounded? Also, in a wye-delta, why is there less distortion in the delta side voltage if neutral in the wye side is not connected to ground? I understand why the Y transformers have distortion and the...

Hi everyone. I'm looking for a derivation of the Spherical Harmonics that result in the form below given in Sakurai's book. I looked up on web and I found just that these are related with Legendre Polynomials. Has anyone a source, pdf, or similar to indicate me? (I would appreciate a derivation...

Homework Statement Here is a copy of the pdf problem set {https://drive.google.com/open?id=0BwiADXXgAYUHOTNrZm16NHlibUU} the problem in question is problem number 1 which asks you to prove the orthonormality of the spherical Harmonics Y_1,1 and Y_2,1. Homework Equations Y_1,1 =...

Hi again, Can/are zig zag connections used on the secondary side to avoid triplen harmonics flowing further up the power system? Let's say 3rd harmonics are flowing up the power system from some loads connected to phases a,b,c and the neutral. Since 3rd harmonic are all in phase, the...

The normalized angular wave functions are called spherical harmonics: $$Y^m_l(\theta,\phi)=\epsilon\sqrt{\frac{(2l+1)}{4\pi}\frac{(l-|m|)!}{(l+|m|)!}}e^{im\phi}*P^m_l(cos\theta)$$ How do I obtain this from this(http://www.physics.udel.edu/~msafrono/424-2011/Lecture 17.pdf) (Page 8)? The...

Homework Statement In t=0, wave function of the particle that moves freely on the surface of the sphere has the wave function: Ψ(Φ,θ) = (4+√5 +3√5cos2θ)/(8√2π) what is time-dependent wave function?Homework Equations Spherical harmonics The Attempt at a Solution I tried normalizing this wave...

Hi, could anyone explain to me how odd harmonics in the power system are reduced or removed? I've read that in transformers the harmonics produced by the load circulate if the secondary side is wired as delta configuration, yet star is usually used on secondary side i believe? I've looked...

Hi Anyone got any suggestions/recommendations for literature either available for free online or books that I have to buy? My background: Electrical engineering student, working on a project that is about analysis of power quality with focus on harmonics.

Hi, I should know better, but I'm having a mental blank. I was just wondering, if you're doing something using non-linear components on the mains, could be anything, maybe bucking to make a DC supply, whatever. Is it common practice to use an isolation transformer between mains and the...

Hi, please help me with the following questions ! can we say that harmonics are because of Reactive Power (i know that one way of controlling harmonics is filtering) ? IF YES, can we control Reactive power by increasing Power Factor ? IF YES it means Harmonics can be controlled by increasing...

Hi all, I've been reading up on the physics of waves in order to better understand what goes on with sound. I'm having difficulties understanding how harmonics are produced in guitar strings. It's probably not as complex as I'm making it in my head, and it's really starting to frustrate me...

I read here: http://static.schneider-electric.us/docs/Motor%20Control/AC%20Drives/8803PD9402.pdf that harmonics cause stray flux losses in transformers, how is this so? Thanks

[SIZE=14px][FONT=Verdana]We know that periodic function can be written in terms of complex Fourier coefficients: $$f(t)=Fn0+\sum_{n=-\infty,n\neq 0}^{n=\infty}F_ne^{jnw_0t}$$, where $$Fn=\frac{1}{T}\int_{\tau}^{\tau+T}f(t)e^{-jnw_0t}dt$$ and $$Fn0$$ is DC component. Power spectrum of signal is...

Simple question, What's the advantage of having more phases in an inverter? Like why have 6 or twelve phases? Is it something to do with harmonics? I know that the higher the switching frequency the further off in the freequency spectrum you can push the harmonics, but I can't see that being...

Homework Statement A fellow student of mathematical bent tells you that the wave function of a traveling wave on a thin rope is y(x,t)=2.30mmcos[(6.98rad/m)x+(742rad/s)t]. Being more practical-minded, you measure the rope to have a length of 1.35 m and a mass of 3.38 grams. Assume that the...

1. Homework Statement Homework Equations Here we have to express ##\psi(\theta,\phi)## in terms of spherical harmonics ##Y_{lm}## to find the angular momentum. If ##\psi(\theta,\phi) = i \sqrt{\frac{3}{4\pi}} \sin{\theta} \sin{\phi} ##, it can be written as: $$ \frac{i}{\sqrt{2}} (Y_{1,1}-...

Hello people ! I have been studying Zettili's book of quantum mechanics and found that spherical harmonics are written <θφ|L,M>. Does this mean that |θφ> is a basis? What is more, is it complete and orthonormal basis in Hilbert? More evidence that it is a basis, in the photo i uploaded , in...

In Dodelson's "Modern Cosmology" on p.241 he states that the ##a_{lm}##-s -- for a given ##l##-- corresponding to a spherical harmonic expansion of the photon-temperature fluctuations, are drawn from the same probability distribution regardless of the value of ##m##. Dodelson does not explain...

What kind of effects that provides to the power lines due to the harmonics? Please consider those harmonics are generated through electronic equipments? Thanks in advance.

When it comes to waves, spherical harmonics are, like, da bomb. I'm no expert - probably obvious from the question - but it seem to me that an instrument which maximises the utilisation of harmonics/resonances would be spherical. And yet, I can think of no spherical instruments - the most...

I am beginer in image processing. Any signal whether it is 1D,2D or any multidimensional signal can be represented using combination of number of sine and cosine wavesforms (harmonics).Similerly any image can be termed as a function of sinusoidal signals.I want to see individual pattern for the...

Lets say I have a switchboard that requires ONLY 3 Phase loads, transformer, UPS, Motors, ETC. ( no neutral is required at all) Now let's say I am feeding this from a generator where I have 4 wires from the alternator ABCN connected to the aforementioned switchboard. the N of the generator...

This is not a homework question per se, but rather something I have come across during a homework project. Using Audacity, I recorded a few different instruments playing the same notes (investigating timbre). I noticed that (using a steel string acoustic guitar) the first harmonic at 131 Hz...

i am a beginner and was going through (Donald Mcquarie's "quantum chemistry" ) some discussion regarding orbitals of H-atom but i didn't get the logic behind writing px and py orbitals as linear combinations of spherical harmonics? according to what i understood, a given spherical harmonic in...

I am studying the Earths main magnetic field (internal, specifically the stuff at the Core-Mantle boundary) which has led me to spherical harmonics. I am curious... how is the structure of a spherical harmonic determined by its degree l and order m? What role do the first three coefficients...

Hello, I am watching a video about spherical harmonics, and I am at the point where the color map is being shown for various values of ##l## and ##m## My question is, what am I supposed to make of these plots? Pretty colors yes, but what do these things mean?

Homework Statement I have a question about the following text: In the red section, if I understand correctly, they're saying that if on a string, there is a musical note being played, the frequency that the note is being played at is called the fundamental frequency. But, if it's at its...

Homework Statement Basically, I was reading the following passage from a textbook, and I'm confused as to why they mention natural frequencies? Doesn't each harmonic have just one frequency that it oscillates at? From what I understand, the natural frequency is just the frequency an object...

I'm a maker of concert-tuned transverse ocarinas, which are a kind of Helmholtz resonator, however that does not tell the whole story as they are driven with an air-reed. This set up seems to differ from what is defined by the Helmholtz resonator equation in that it does not have a single...

Hi I want to ask you if you know hot to write cos(theta)cos(phi) in terms of spherical harmonics? Thanks

Homework Statement An acoustic signal is composed of the first three harmonics of a wave of fundamental frequency 463 Hz. If these harmonics are described, in order, by cosine waves with amplitudes of 0.100, 0.300, and 0.760, what is the total amplitude of the signal at time 0.401 seconds...

Hi Folks, The Fourier Cosine Transform of cos(x) for 0<x<a and 0 everywhere else is given as F(\omega)=\displaystyle\frac{1}{\sqrt{2 \pi}}[\frac{\sin a (1-\omega)}{1-\omega}+\frac{\sin a (1+\omega)}{1+\omega}] I can plot this and we get a continuous amlitude spectrum of F(\omega) against...

Homework Statement Well it is not the problem itself that bothers me but the maths behind a part of it. As part of finding the coefficient I had to solve the integral of (Sin(x))^(2l+ 1). The solution given by the solution manual just pretty much jumps to the final answer...

Hello, I am having a hard time solving this question. Any help is really appreciated. 1. Homework Statement You have designed a new musical instrument of very simple construction. Your design consists of a metal tube with length L and diameter L/10. You have stretched a string of mass per...

how do I to change the harmonic of a sin wave ? I want it to sound more like a real note. I tried this : buffer[n] = Amplitude * Math.Sin(Math.PI * Frequency * n / 44100D) + (Amplitude/2 * Math.Sin(Math.PI * Frequency/2 * n / 44100D)) + (Amplitude/2 * Math.Sin(Math.PI * Frequency *2 * n /...

Homework Statement A pipe resonates at successive frequencies of 540 Hz, 450 Hz, and 350Hz. Is this an open or a closed pipe? Homework Equations -- The Attempt at a Solution My assumption is that because the harmonics of an open pipe are odd number multiples of the fundamental frequency (1f...

1. The problem statement,λ all variables and given/known data A drum skin is stretched over one end of a pipe, creating a resonant air column with one open end and one fixed end. How long must the pipe be to achieve a resonant frequency of 280.0 Hz? (Use 343 m/s for the speed of sound.)...

Homework Statement A violin has four strings that are 32 cm long and are typically tuned to concert G, D, A, and E (196 Hz, 294 Hz, 440 Hz, and 660 Hz). A)What is the wavelength of the fundamental mode of oscillation on the A string? Sketch the waveform. B)What is the wavelength of the sound...

A serie RLC Circuit consists of 20ohm Resistor, an inductor with an inductance of 130mH and a variable capacitor. The capacitor is set to give resonance to the circuit at the third harmonic. The instantaneous value of the sinusoidal voltage across the circuit is represented by v(t) = 78 +...

I had a chance to go through a lecture on general NVH issues in Automobile engineering. The faculty used to say "first harmonic", "second harmonic" etc. during the course. I found in wikipedia to know that harmonics are multiples of frequency of vibration. What has harmonics got to do in NVH...

Hello, As a science writer, I've tasked myself with acquiring a thorough theoretical and historical understanding of Quantum Mechanics. It would be interesting to know if there has ever been any experimental verification of Laplace's spherical harmonics, relating to the quantum mechanical...

Hey guys, This is my first post here, so I will apologize in advance in case I'm posting this in the wrong section. I wrote a very simple function to calculate spherical harmonics in matla, and I used this function during 3 years. Yesterday I found that the function was actually wrong, and...

Homework Statement When an instrument plays a note, the resulting sound is a combination of all the possible harmonics for that instrument in its momentary configuration. For instance, a musician changes notes on a violin by pressing the strings against the neck of the instrument, thus...

Hi. http://www.nt.ntnu.no/users/jensoa/E-FY1006-31mai2012.pdf Please open the link and go to page 11, problem 3. It appears, after all, I understand nothing when it comes to the wave function of Hydrogen like atoms. So I kindly ask you to answer some questions I got: 1) "A selection of these...

If the B-mode sky plots could be Fourier transformed what would be a plot of the lowest order B-mode harmonic plotted on a sphere look like? I guess we need two functions of spherical coordinates, one function for amplitude at points on a sphere and one function for the orientation at the...

Homework Statement I want to show that <n',l',m'|\hat{z}|n,l,m> = 0 unless m=m', using the form of the spherical harmonics. Homework Equations Equations for spherical harmonics The Attempt at a Solution Not sure how to begin here since there aren't any simple eigenvalues for...