Harmonics Definition and 281 Threads

Homework Statement What fraction of the energy of a square wave is in its fundamental? In its first five harmonics? First seven? Nine? Homework Equations the Fourier series of a square wave... v(t) = ( 4V / pi ) ( sinw0t + 1/3sin3w0t + 1/5sin5w0t + ... ) also given a graph showing...

Homework Statement A. A string with a mass density μ = 4.10×10-3 kg/m is under a tension of F = 327 N and is fixed at both ends. One of its resonance frequencies is 742.0 Hz. The next higher resonance frequency is 1113.0 Hz. What is the fundamental frequency of this string? B. Which harmonic...

Homework Statement An organ pipe is 1.70 m long and it is open at one end and closed at the other end. What are the frequencies of the lowest three harmonics produced by this pipe? The speed of sound is 340 m/s. Only one answer is correct. 200 Hz, 400 Hz, 600 Hz 200 Hz, 300 Hz, 400 Hz 200...

This isn't exactly a part of any problem, but a part of a generic principle. I don't understand the use of raising and lowering operators. L_{^+_-}=\hbar e^{^+_- i l \phi}({^+_-}\frac{\partial}{\partial \theta}+ i cot \theta \frac{\partial}{\partial \phi}) So how does one use L_{^+_-}Y_l^m...

Homework Statement I want to expand 1+sin(phi)sin(theta) in the spherical harmonics. I am not sure if this will be an infinite series or not? If it were infinite that would seem rather difficult because the spherical harmonics get really complicated when l > 3. Also, all of the sine terms in...

Homework Statement Finding the potential. Homework Equations general solution of potential is in terms of spherical harmonics Y_l,m. The Attempt at a Solution My question is how do we know which l to choose given a boundry condition. for example if the potenial on the surface of...

I'm having a bit of a difficulty trying to determine the fundamental frequency in a given function and the harmonics. In the equation below,would the fundamental frequention be 1 (corresponding to the value cos(1x-pi)) and the harmonics amplitude 3 and -4?Also,the values of the frequency of the...

Homework Statement The spherical harmonics Y^m_l with l=1 are given by Y^{-1}_1 = \sqrt{\frac{3}{8\pi}}\frac{x-iy}{r}, Y^0_1 = \sqrt{\frac{3}{4\pi}}\frac{z}{r}, Y^1_1 = -\sqrt{\frac{3}{8\pi}}\frac{x+iy}{r} and they are functions of L^2 and L_z where L is the angular momentum. i) From...

Harmonics of a Square Wave... Homework Statement A 200kHz square wave with a fundamental frequency amplitude of 15V. Find amplitude of the third harmonic. Homework Equations This is what I do not know. I know this is a Fourier transform problem but just don't know what to do with...

Homework Statement A 8.3 kg mass slides on a frictionless surface and is attached to two springs with spring constants 28 N/m and 62 N/m that are on either side of the mass. Find the frequency of oscillation. Answer in units of Hz. Homework Equations (2pi sqrt(m/k))^-1 The...

String A is stretched between two clamps separated by distance L. String B, with the same linear density and under the same tension (i.e., having the same wave velocity) as String A, is stretched between two other clamps separated by distance 4L. Consider the first 8 harmonics of string B. For...

i'm a flautist. sometimes i have to play notes called harmonics, where the finger position is the same (i.e. same holes closed off) but you have to vary the air speed so that you can hear the original note and also another note above it in pitch. can anyone explain to me why it is that i can...

Hi, I'm trying to get the Y_l^l spherical harmonic and I'm running into problems evaluating the following expression: \frac{d^{2l}(\cos^2(\theta) - 1)^l}{d\cos(\theta)^{2l}} The 2lth derivative with respect to cos theta of cos squared theta - 1 to the lth power it just seems like I'm going...

Hi, I am a bit puzzled by a physics problem. I had to calculate the force on a wire and its second harmonic. Given data were, the diameter of of the string 1,2 mm , length of 1,25m. Density of steel 7,8 kg/dm^3, its fundamental frequency is 300 Hz, and also one end is fixed the other is...

Happy New Year all! i have a question regarding the addition theorem for spherical harmonics. In JD Jackson book pg 110 for e.g. the addition theorem is given as: P_{L}(cos(\gamma))=\frac{4\pi}{2L+1}\sum_{m=-L}^{L}Y^{*}_{Lm}(\theta',\phi')Y_{Lm}(\theta,\phi) where...

In finding harmonics do you just multiply the harmonic number times the frequency? Find the first four harmonics when f=343Hz would be f1=343Hz, f2=686Hz, f3=1029Hz, and f4=1372Hz. This just seems too easy.

I'm calculating the zz Component for the quadruple tensor. Q_{zz} = 3cos^2\theta-1 (r=1 in this case), and the Y_{lm}(\theta,\phi) would be l=2, m=0. I would like to calculate the result in either maple or mathematica - I have not used either very much - I want to check the result using...

In solving the 3D hydrogen atom, we obtain a spherical harmonic, Y such that, Y_{lm}(\theta,\phi) = \epsilon\sqrt{\frac{(2l+1)}{(4\pi)}}\sqrt{\frac{(l-|m|)!}{(l+|m|)!}}e^{im\phi}P^m_l(cos \theta) where \epsilon = (-1)^m for m \geq 0 and \epsilon = 1 for m \leq 0 . In quantum, m = -l...

Ok, I was given a question in homework and was never told the right answer. If the Fundamental Frequency = 15Hz, the 3rd Harmonic = ? I estimated it at 45Hz because of an example The example was; Harm 1 = 100 x 1 = 100Hz Harm 2 = 100 x 2 = 200Hz Harm 3 = 100 x 3 = 300Hz If so...

I understand that harmonics are integer multiples of a fundamental frequency. Also, that the relative strengths of the harmonics are what make the same note on different instruments sound different. Why are these other frequencies made? How many integer multiples are there? Why do our...

I have recently come across the subject of harmonics in my new job and I am a little puzzled about them. I understand that they are produced by devices which draw current in a non-linear fashion and that they can travel throughout a network causing items to overheat and such like. BUT... I...

There is this excersise in Griffith's QM text that I can't seem to solve. It's about the calculation of the normalization factor of the spherical harmonic functions using the angular momentum step up operator. These definitions/results are given: Y_l^m = B_l^m e^{im\phi} P_l^m (\cos\theta...

So let us assume we have the following system. A harmonic oscillator consists of a mass 1g on a spring. Its frequency is 1 Hz and the masses passes through the equilibrium position with a velocity of 10cm/s. I have already calculated that the magnitude of the quantum number (n = 7.6 x 10^27)...

Complex waves... I have learned that with a musical instrument you set up standing waves of the fundamental frequency as well as other harmonics which cause the specific "quality" of the sound - my question is why do you produce different harmonics and not just the fundamental frequency? When...

Hello, My question is fairly simple. My instructor solved in class today Laplace's equation in spherical coordinates which resulted in spherical harmonics. I have not taken any quantum mechanics yet so this is my first exposure to spherical harmonics. What do the "l" and "m" terms in the...

Hi We just did a lab on waves and one in particular I'm unsure about. We set up standing waves on a spring and observed the period of each successive harmonic. It was found that the period was cut in half with each harmonic. Or the frequency was doubled. ie. harmonic 1 produced one...

Greetings, I´m calculating cuadratic dispersion of some quantum systems. I need to expand x^2 in terms of spherical harmonics (using Clebsch-Gordan coefficients, or threeJ as well) in order to be able to use Gaunt espression in the integral solving. I start from the expansion of x as...

so IN THEORY, there should be an oscillation pattern that yields the hydrogen spectrum ?

Viva! I wonder if anyone could explain me the difference between real spherical harmonics (SH) and complex SH. What's the difference in doing an expansion in either situations? And what are the orthogonality relations for each case? Any help would be great...( websites, books..)...

Dear Members of Physics Forums Cosmology Let me introduce myself. My name is Ray Tomes and after a career in computer software development and computer modelling I have spent about 15 years in full time study of cycles in many different disciplines including astronomy, geology, biology...

Can someone explain to me precisely what harmonics are, and the technical differences between even and odd numbered harmonics?