Fundamental Definition and 947 Threads

Homework Statement A uniform string of length 2.5 m and mass 0.01 kg is placed under a tension of 10 N. 1. What is the frequency of the fundamental mode? 2. If the string is plucked and is then touched at a point 0.5 m from one end, creating a node, what frequencies persist? Homework...

Is the fundamental frequency considered an odd harmonic? Thanks for any clarification

Fundamental Frequency (String Resonance) - velocity problem! Homework Statement Hey guys, i just started working on Fundamental Frequency but am getting confused! A string that is 6.0m long is vibrating with three loops in it. The frequency of the source is 16.5Hz. A)What is the...

I have been given data for the Coma and S639 clusters, including their velocity distances. For part a I calibrated the fundamental plane using the Coma data, and got: log(Re) = 1.24log(\sigma) - .82log<I> - .259 I am now supposed to use the S639 data along with the above fit to get a distance...

Homework Statement prove that the limit of anxn + an-1xn-1 + ... + a1x1 + a0 as x goes to infinity equals infinity ** I forgot to mention that n is an odd number and this is for n>0 otherwise yes your counter example would be correct** Thanks for the quick responses by the way Otherwise, that...

How do you compute the Fundamental group of the 1-skeleton of the 3-cube I^{3} = [0,1]^{3} ? What about the Fundamental group of the 1- skeleton of the 4-cube I^{4} ? I know the Fundamental group of a space X at a point x_{0} is the set of homotopy classes of loops of X based at x_{0} . And...

This question may be one of those questions that is hard to talk about because it seems so obvious that a certain thing has to be a certain way that it becomes impossible to figure out how you know that it has to be that way. When you derive the Lorentz transformations from a certain set of...

I am curious how exactly fundamental measurements are made for subatomic particles. I am hoping someone who knows can point me to some references as to the following: 1) How is the position of a photon measured? 2) How is the position of a subatomic particle measured? 3) How is the momentum...

i was wondering if anyone could point me towards any resources (including books, papers, and/or notes) that discusses and explicitly derives the fundamental solution to the radial wave equation. i have evans' PDE book, but it isn't contained there, and I've been having trouble searching for it...

Hello all, I am going through some sample problems exercises in Paul Sally's Tools of the Trade, and am being asked to prove the Fundamental Counting Principle. That is, If A has m elements and B has n elements, then A X B has mn elements. Sally goes on to write that "this is simple to prove...

Homework Statement I am familiar with the following kind of conditional expectation expression: \mathbb{E}[Y|X=x], where X and Y are random variables. I am wondering what the following conditional expectation stands for: \mathbb{E}[Y|X] How these two are related? How the second...

How to find the fundamental frequency of the component(let it for engine)? How the orders of that frequency is approximated while FEA?

Homework Statement A license plate has three letters followed by three numbers. Suppose the digits from 0...9 can be used, except all three digits cannot be zero, and that any letter from A-Z with repeats can be used. How many plates are possible? Homework Equations My question is on...

Hi, how can i derive this fundamental identity "without using entropy"? \left(\frac {\partial U}{\partial V}\right)_T = T\left(\frac {\partial P}{\partial T}\right)_V - P I believe the above equation is purely thermal and has nothing to do with entropy and statistical mechanics but...

If Quantum mechanics theory is the most fundamental theory of nature that explain it at the smallest scale then it should explain Consciousness . I think that there may be deeper level of physics that can explain it . If consciousness is merely a quantum effect , it may be not only limited to...

So I was thinking about the question "What if Boltzmann's constant k were different?" but then I got thinking about the nature of the question. What is the significance of a constant? Can you say one dimensioned constant is more fundamental than the other one? For example, I can imagine...

All the fundamental forces are acting all the time, weak decays etc. So we need colliders so we will have more events per unit time for better analysis? What is the higher energy for? Proton collison of 14 TeV should "blow" the Higgs out for us to see? In general, how does higher energies...

Can we apply the fundamental theorem of calculus to an integrand that's a function of the differentiating variable? For example, can one still use the fundamental theorem of calculus when trying to find the derivative of this function: f(x) = \int_{0}^{x} \frac{cos(xt)}{t}dt

Homework Statement When a 70kg aluminum (density = 2.7 g/cm3) sculpture is hung from a steel wire, the fundamental frequency for transverse standing waves on the wire is 250.0 Hz. The sculpture (but not the wire) is then completely submerged in water. What is the new fundamental frequency...

The fundamental group of a torus is Z*Z,then the fundamental group of a punctured torus is Z*Z*Z. But I've ever done a problem,it said a punctured torus can be continuously deformed into two cylinders glued to a square patch.Really? If that is right,then the fundamental group of punctured...

Homework Statement Theorem. (Fundamental Theorem of Arithmetic) Ever positive integer n has a prime factorization, which is unique except for reordering of the factors. Homework Equations 6.8 Definition. A prime factorization of n expresses n as a product of powers of distinct primes; the...

Quantum mechanics is a very powerful and accurate method of describing the actions of small particles in space but it has its limits. On the large scale, QM cannot explain relativistic effects. On the smallest of scales, the theory starts to become nonsensical. QM is based on events whch are...

Everyone knows by now that a conic section is the figure formed when a plane intersects a right circular cone. Most everyone also knows that there are many different ways to describe a conic, geometrically and algebraically. What one seldom sees is the derivation of those descriptions from the...

Almost all physics or engineering textbooks have a table of the SI units that are based on six fundamental quantities. The one that is listed for the quantity "electric current" is always "ampere". However, usually a few pages past this fundamental table lies a definition of the ampere. 1...

To proove the inequality: \left | \int_a^b f(t) dt \right | \le \int_a^b | f(t) | dt for complex valued f, use the following: \textrm{Re}\left [ e^{-\iota\theta}\int_a^b f(t) dt\right ] = \int_a^b \textrm{Re}[e^{-\iota\theta}f(t)] dt \le \int_a^b | f(t) | dt and then if we set: \theta =...

I am seeking to understand the relationship of energy within a standing wave vs. the energy in its first three harmonics. Is the energy latent within the fundamental wave the same as the energy in its first three harmonics, or is the energy and exponential increase. IE How much energy is...

How were the masses of fundamental particles(electrons,protons,neutrons) determined?

Hi. So I have learned that this holds for the trace if A and B are two operators: \text{Tr}(AB)=\text{Tr}(BA). Now I take the trace of the commutator between x and p: \text{Tr}(xp)-\text{Tr}(px)=\text{Tr}(xp)-\text{Tr}(xp)=0. But the commutator of x and p is i\hbar. Certainly the trace of...

Hi, I've been watching the MIT lectures on single variable calculus, and whilst proving FTC, he mentions that we since we know that: <$> f'(x) = g'(x) </$>, then by MVT we know that <$> f(x) = g(x) + C </$>. I have tried searching for somewhere where this implication is spelled out for me...

Are forces due to fields or are fields an abstraction of forces? Do electromagnetic waves exist apart from as an abstract description of changing fields, which are in turn abstract descriptions of changing forces (or potential of force if there was an object for force to be applied to)?

What do we mean by different fundamental forces having different relative strength? And if we already consider electromagnetic and weak interaction to be different manifestations of the same force, how are their relative strengths different?

Problems with fundamental particles and quarks :( Hi, I have no idea where to post this so I hope its ok... I'm studying A level physics. We have a topic on fundamental particles. Yea couple of questions... 1. Whats the difference between a (insert lepton here)-neutrino, and its...

Is rest mass just an illusion? In Proton, for example, most of the rest mass is relativistic mass of quarks, moving at relativistic speeds. Quarks are quite light, but if we go deeper, the rest mass of quark is also an illusion - all particles have rest mass = 0, and what we call mass is...

Homework Statement Consider a cartesian coordinate q_k and conjugate momentum p_k. The Poisson-bracket for two random functions f=f(q_1,..,q_f,p_1,..,p_f,t) and g=g(q_1,..,q_f,p_1,..,p_f,t) is defined as: \{f,g\}=\sum_{i=1}^{f}\biggl(\frac{\partial f}{\partial q_i}\frac{\partial g}{\partial...

Homework Statement Verify that y1(x) = 1 and y2(x) = x^.5 are solutions of the following y y'' + (y')^.5 = 0. Then show that c1 + c2 x^.5 is not in general a solution of this equation. Homework Equations The Attempt at a Solution I was able to show that both y1 and y2 are...

How do you define what is a fundamental circuit element? I am not really sure, why isn't a transistor a fundamental circuit element. Can u consider a switch a fundamental circuit element or is it a resistor with infinite resistance.

Homework Statement a) Use the fundamental theorem of line integrals to evaluate the line integral: ∫(2x/(x^2+y^2)^2)dx+(2y/(x^2+y^2)^2)dy (over C) Where C is the arc of the circle (x-4)^2+(y-5)^2=25 taken clockwise from (7,9) to (0,2). Explain why the fundamental theorem can be applied. b)...

I would like a reference for a purely algebraic proof of the fundamental theorem of algebra - or if you would like to supply a proof that would be even better.

Homework Statement View S^3 as the unit sphere in C^2. Now, 1. What are the path connected components of the subset of S^3 described by the equation x^3 + y^6 = 0, where the x and y refer to the coordinates (in C)? 2. Is it true that the similar subset x^2 + y^5 = 0 is homeomorphic to...

In a smooth compact 3 manifold there is an embedded loop - a diffeomorph of the circle Consider a torus that is the boundary of a tubular neighborhood of this loop. If the loop is not null homotopic does that imply that the torus is not null homologous?

Is there such a concept in information theory? I.e. Something as complex as language can be reduced to 1's and 0's. Is binary the fundamental unit of information?

I'm just trying to get a few things straight as I delve into the world of quantum physics and string theory. First of all, what does it mean when someone says two forces combine, such as the electromagnetic and weak force as the electroweak force? Does that mean that the particles are the same...

If I take a plane with n holes, would the fundamental group be that of the "bouquet of n circles"? (http://en.wikipedia.org/wiki/Rose_(topology ).) The bouquet of circles is the same as the unit line with n-1 points identified. All three spaces initially appear quite different so it would be...

I am doing some revision and trying to do fundamental groups and I was wondering if the fundamental group of the following space is {1} i.e. all loops based p are homotopic. fundamental group of (X,p) = D^2\{(x,0) : 0<=x<=1} where p=(-1,0)

I just don't get it. Some people, deep down in their hearts, want to see computation as the most fundamental thing ever. This is the reasoning behind the holographic idea, at least from Verlinde. Variable spin makes it possible quantum computation through anyons, yet people still want spin like...

What I understand from the definition of the fundamental group is: Pi1(X.x) is "the set of rel {0,1} homotopy classes [a] of closed paths" Ok, when I think about one [a] it consists of all: 1.Closed paths like a and b with a(0)=a(1)=x & b(0)=b(1)=x --->since they are closed. 2.And since...

Homework Statement Determine the Fundamental Period and Frequency I got this question wrong on My midterm and I was wondering if you guys could give me some feedback on it x(t) = cos[50(pi)t] + sin[15(pi)t] Homework Equations T(fundamental Period) = 2(pi)/w // w is the frequency...

Can someone explain to me the fundamental understanding of why, when two hydrogen atoms for example, release energy when they form a covalent bond? I can't seem to comprehend. Here is my reasoning, please see if this makes any sense of I am simply going in the wrong direction, I would really...

Does all energy storage occur in fundamental forces or bonds? I believe that a rubber band stores energy in the electrical bonds between the molecules. Same with a spring. In the atom, energy is stored and released from the electrical bonds between electrons and the nucleus during photon...

What restrictions must we place on a real-valued function F for F(x) = \frac{d}{dx} \int_a^x F'(y)dy to hold, where "\int" is the Lebesgue integral?