Harmonics Definition and 281 Threads

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...

I feel like the various members of the world of physics don't agree upon what the values of n, harmonics, and overtones line up for STOPPED pipes where f n = nv / 4L According to my physics textbook (University Physics Young and Freedman), for stopped pipes, 3rd harmonic = n is 3 = second...

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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...

Homework Statement a 32 cm violin string with linear mass density is .36 gm/m is placed near a loudspeaker that is fed by an audio oscillator of variable frequency. It is found that hte string is set into oscillations at frequencies 1320 Hz and 1760 Hz as the frequency of the audio oscillator...

Hi, I have build an 12VDC- 12VAC inverter using a square wave gate signal for my power MOSFETs. My output is perfect square wave and now i want to clear the harmonics except the fundamental. I am not sure how can i design the analog filter that can filter the harmonics except the...

Could someone validate if this is correct? for waves with antinode/antinode or node/node ends if the fundamental frequency is f1 then f2 = 2f1, second harmonic and f3 = 3f1, third harmonic but for waves with antinode'/node or node/antinodes at the ends then if fundamental frequency is...

Homework Statement A steel rod of length 1.44 m is clamped at a point 1/4 of its length from one end. The ends of the rod are free to vibrate. If the velocity of longitudianl wave in steel is 5000 m/s, find the frequency of the first three allowed harmonics. Make diagrams to show the three...

Homework Statement A system's wavefunction is proportional to sin^2p. What are the possible results of measurements of Lz and L^2? Give the probabilities of each possible outcome. I'm using p for theta and q for phi. Homework Equations The Attempt at a Solution So I believe that the value of...

This is something I wanted to do, but I don't know where to start. Given an alternating signal (not necessarily sinusoidal) if you wanted to double the frequency of the signal, where would you start?

Homework Statement The angular part of a system’s wavefunction is <\theta, \phi | \psi>\propto (\sqrt{2}\cos\theta + \sin{\theta}e^{−i\psi} - \sin{\theta}e^{i\psi} ). What are the possible results of measurement of (a) L^2 , and (b) L_z , and their probabilities? What is the...

Homework Statement Given the first harmonic, with length L, of a certain standing wave, what is the process for coming up with the next 3 harmonics for it?Homework Equations velocity = wavelength * frequencyThe Attempt at a Solution I don't understand how to draw the "next harmonic". I've come...

Am I correct in stating that the number of *anti nodes* in a STRING denotes the harmonic and the number of *nodes* in a OPEN TUBE denotes the harmonic? -Thanks

Homework Statement Hi! I need help with this. I have to calculate the expression of a function using spherical harmonics. The relevant equations are given below. An example of a function can be f(theta,phi) = sin(theta)... Can you help me to calculate de coeficients and to express the...

Homework Statement A flute is essentially a pipe open at both ends. The length of a flute is approximately 66.3 cm. The speed of sound in the flute is 342 m/s. What is the first harmonic of a flute when all keys are closed, making the vibrating air column approximately equal to the...

Dear people. I am working on music theory and I am making a program to derive musical scales, but I need a name for the interval of combining to harmonic intervals. Etc. if I multiply 4/3 with 5/4 I get 5/3. But what is the correct words for such intervals (except that a few of them actually...

"simple" simple harmonics question in a recent lab experience of simple harmonics, pendulum motion, we find that as the length of the pendulum is deceased the period changes but the real question is about the velocity of the pendulum as the length is decreased. when graphing the length over...

Whats a good book to learn about these topics?

Hey, this is going to be abit long winded... In a Stern-Gerlach experiment a beam of hydrogenic atoms in the l=1 state traveling along the y-axis is first passed through an inhomogeneous magnetic field in the z-direction to yield three beams corresponding to three eigenstates Y(z,1), Y(z,0)...

I would appreciate some input about how to program spherical harmonics in Matlab. http://mathworld.wolfram.com/SphericalHarmonic.html I want to program a double summation that looks like this. G(\Omega_{1},t_{1}|\Omega_{0}) = \sum_{l=0}^\infty \sum_{m=-l}^l...

Homework Statement A problem with odd harmonics only. Show that the solution of the heat equation du/dt=c2*(d2u)/(dx2), subject to boundary conditions u(0,t)=0 and ux(L,t)=0, and the initial condition u(x,0)=f(x) , is u(x,t)= \sum Bnsin[(\pi/2L)(2n+1)x]e-((c*\pi/2L)*(2n+1))^2 where n...

expansion of polarized plane waves into spherical harmonics, please help! Hi all, I would like to get some guidance in how to expand a polarized (i.e. linear polarization) plane wave into a series of spherical harmonics. I am aware of the formula applying to scalar plane waves (please see...

Homework Statement A 2.40 kHz sound wave is transmitted through an aluminum rod. A) What is its wavelength in the aluminum? B What is the sound wave's frequency when it passes into the air? C) What is its wavelength in air? The speed of sound in aluminum is 5100 m/s according to the...

I wonder if you can recommend a good book treating "Spherical Harmonics" in some details. Thanks for help

Would a harmonic of the Larmor frequency have any effect on proton precession?

Describing the a model Two hands of an analog clock: r1 (hand of the minutes) and r2 (hand of the hours), and a relative vector r21 between them. The question: In spherical harmonics representation how can I describe the motion of the vector r21 by the rotation of r1 relative to r2 (r2 is...

Hello, I am confused in some areas of this topic at school and i was wondering if you guys knew any good tutorials online that i could learn from. Tried a few sites but they are "wayyy" above my head. The things i need to know is like, the angles in radians, diplacenment, acceleration, speed...

Homework Statement The frequency of a tuning fork can be found by the method shown in Figure 13-24. A long tube open at both ends is submerged in a beaker of water, and the vibrating tuning fork is placed near the top of the tube. The length of the air column, L, is adjusted by moving the...

A high voltage capacitor is charged and then the two leads are shorted together generating a spark, simultaneously a nearby radio crackles. This shows us that when the spark was generated radio waves was also generated. These primitive radio waves are sometimes called hertzian waves. A bolt of...

[SOLVED] Open ended pipe Harmonics Mastering Physics Question Homework Statement Consider a pipe 45.0cm long if the pipe is open at both ends. Use v = 344m/s. Now pipe is closed at one end. What is the number of the highest harmonic that may be heard by a person who can hear frequencies...

Homework Statement A SHM motion can be described by a=-400x. The amplitude is 8cm. Find the displacement and acceleration at a time of 2s. Homework Equations x = A sin(2pi f t) x = A cos(2pi f t) a=-(2pi f)squared*x The Attempt at a Solution Firstly I realized that 400=2pi f , so f...

The question is exactly this: Prove that the maximum speed (Vmax) of a mass on a a spring is given by 2(pi)fA. where f = frequency and A =Amplitude We are given such formulas as: f=[1 / 2(pi)]square_root (k /m) or f=[1 / 2(pi)]square_root (a /-x) the formula for total energy in a...

If you vibrate a tuning fork over a closed pipe (a pipe with one end closed and the other open) is it possible to get overtones in the pipe even thought the tuning fork only vibrates at one frequency For example if you have a tuning fork of freq 300HZ and you allow it too vibrate above a closed...

I have been torturing myself with this problem for a couple weeks now and I am stumped. The unit I am working on is called simple harmonics. The question is: Prove that the maximum speed (Vmax) of a mass on a spring is given by 2(pi)fA I am guessing that the question wants me to re-arrange one...

Right, I'm new to this forum but not new to asking daft questions. So here we go. Just Imagine I'm sat in my shed and I've got a battery hooked up to a purely resistive load with a switch between the two. In adition I've set up a tuneable antenna in close proximity. If I turn the switch...

[SOLVED] Plz help w/ Simple harmonics question I am doing simple harmonics and running into problems. The formulas given for simple harmonis in my book are f=[1 / 2(pi)]square_root (k /m) or f=[1 / 2(pi)]square_root (a /-x). The question reads: Car 1 has a...

Homework Statement A tuning fork is set into vibration above a vertical open tube filled with water, as seen in the figure below. http://capaserv.physics.mun.ca/giancoli-calc/Graphics/Graph16/dgian1686.gif The water level is allowed to drop slowly. As it does so, the air in the tube above...

That is all that is needed, three would be too complex, one can get the harmonics from two, it hard to imagine there being three, but may be the third is an echo ?

Homework Statement Consider a small (sub-threshold) signal on a nerve fiber or a telegraph cable. The signal can be written as a sum of "harmonics" V(x,t) = \sum(V_{n}cos(k_{n}x)f_{n}(t) where n is some index identifying the terms, the V_{n} are constants, the k_{n} are wave numbers for...

Homework Statement Consider a small (sub-threshold) signal on a nerve fiber or a telegraph cable. The signal can be written as a sum of "harmonics" V(x,t) = \sum(V_{n}cos(k_{n}x)f_{n}(t) where n is some index identifying the terms, the V_{n} are constants, the k_{n} are wave numbers...

Homework Statement Why is is the for physical applications of the spherical harmonics |m| must be less than or equal to l, with both being integers? Homework Equations Y(m,l)=exp(im phi)P{m,l}(cos theta) Hopefully my notation is clear, if not please say. The Attempt at a Solution Well...

Homework Statement At t=0, a given wavefunction is: \left\langle\theta,\phi|\psi(0)\right\rangle = \frac{\imath}{\sqrt{2}}(Y_{1,1}+Y_{1,-1}) Find \left\langle\theta,\phi|\psi(t)\right\rangle. Homework Equations \hat{U}(t)\left|\psi(0)\right\rangle =...

[SOLVED] Simple Harmonics Homework Statement A 10.0 kg mass is traveling to the right with a speed of 2.40 m/s on a smooth horizontal surface when it collides with and sticks to a second 10.0 kg mass that is initially at rest but is attached to a light spring with force constant 75.0 N/m...

Homework Statement I want to expand sin(theta) in spherical harmonics. Well, actually I want (3cos^2(theta+45°)-1)*exp(i*(psi+45°)) but I think I could find my mistake by the above simple example. Homework Equations http://en.wikipedia.org/wiki/Spherical_harmonics The Attempt at...

[SOLVED] Simple Harmonics - Kind of wierd Homework Statement Question: A 1.30 kg mass on a spring has displacement as a function of time given by the equation: x\left( t \right) = \left( {7.40\;{\rm{ cm}}} \right)\,\cos\:\left[ {\left( {4.16\;{\rm{ s}}^{ - 1} } \right)t - 2.42}...

[SOLVED] Simple Harmonics Question Homework Statement A 1.40 kg ball and a 2.20 kg ball are glued together with the lighter one below the heavier one. The upper ball is attached to a vertical ideal spring of force constant 170 N/m, and the system is vibrating vertically with amplitude 19.0...