Fundamental Definition and 907 Threads

Homework Statement The elements of f(t) are 1+kt and t here are 0<t<1 the other element is 1 and t here are 1<t<2. f(t+2)=f(t) prove if k is not equal to zero, the period f is 2. i know the graph of element 1 but how should I graph the other element with k. Based from the graph...

The Law of Biot and Savart Law tells us how to find a differential form that generates the first de Rham cohomology of S3- embedded loop. Run a steady current through the loop. This form is just the dual of the induced magnetic field (using the Euclidean metric). Ampere's Law tells us...

Homework Statement Is the Fundamental group of the circle (S^1) abelian? Not a homework question, just something I want to use. Homework Equations The Attempt at a Solution Intuitively it appears to be and it is isomorphic to the additive group of integers which is abelian. I...

Homework Statement The function is defined on (-infinity, +infinity) Find the fundamental period of sin(5t+\pi) Homework Equations The Attempt at a Solution f(x)=sin(5t+\pi) f(x)=f(x+2p) f(x+2p)=sin(5t+\pi+2p) f(x+2\pi/5)=sin(5t+\pi+2\pi/5) The period i got was...

Can someone please explain this to me. Let X = fundamental group of a genus 2 surface Let Y = fundamental group of a genus 1 surface Can X embed Y? Ty

So I have been wondering, what is the fundamental group of a projective plane after we remove n points? I tried doing this using Van Kampens Theorem, maybe I am applying in incorrectly, I am getting that it is the Free group on n generators. However, when I think of RP^2 as a quotient of...

Is conservation laws are more fundamental than Newton's second law in Newtonian mechanics? I know from the point of view of Noether's theorem conservation laws are more fundamental. But all the conservation laws can be derived from the F= ma equation. And from these conservation laws I can't...

So the question goes like this- The fundamental frequency of a bass violin string is 1045 Hz and occurs when the string is 0.900 m long. How far from the lower fixed end of the bass violin should you place your fingers to allow the string to vibrate at a fundamental frequency 3 times as great...

Homework Statement Prove \int_{V}\nabla\ T d\tau\ = \oint_{S}Td\vec{a} Homework Equations Divergence theorem: \int_{V}(\nabla\bullet\vec{A})d\tau\ = \oint_{S}\vec{A}\bullet\ d\vec{a} The Attempt at a Solution By using the divergence theorem with the product rule for...

Hi all, First post here for me. 1. Problem Statement Find the fundamental period of: 3cos(1.3PiN) - 4sin(0.5piN +0.5Pi) 2. Relevant equations: T = 2PI / w 3. My attempt: Not sure how to proceed. By themselves the fundamentals period would be: 3cos(1.3PiN) w = 1.3Pi...

What does it mean to say that the fundamental relation of thermodynamics is homogeneous first-order? I struggle with the abstraction of mathematical definitions and, I'm really seeking more to understand the relation of the physical variables of thermodynamics. Why are all of the variables...

OKay so here are two examples: let say 1) f(x) = cos 2x + cos x how do you determine whether this function is periodic? I know I have to find period for each cosine. The first one is pi and second is 2pi. Then what do you do? And eventually, how do you determine the fundamental period...

Can someone please clarify beta decay for me. As I understand it, in B- decay, a neutron turns into a proton, electron, and anti-neutrino, then the electron and anti-neutrino are ejected. But from this example, it looks like there are two additional electrons as a result of decay. 19/8 O ->...

Homework Statement Heres the question: f(t) = Integral from c to t of a(s)ds, and h(t) = ef(t) Compute h' (t) using: 2 fundamental theorems of Calculus and The Chain Ruleany help please ? Homework Equations Fundamental Theorems of calc g(x) = Integral from a to x of f(t) dt and...

I’ve been thinking about comments made by Fra in a number of threads, where he raises questions like – what does an observer “see” at the sub-atomic scale? We could make a long list of more and less reputable ideas about the fundamental information-processes in physics, going back to Wheeler’s...

Problem number 4 on the image has me stumped. I understand the problem (obviously not enough) and what its saying, I'm just having trouble putting it into a proof. Can i get a hint to get me started? Thanks http://img40.imageshack.us/i/asdasdjql.jpg/"

Hi when a system C is composed of two subsystems A and B each described by states spaces Ha and Hb then we are told that the state space corresponding to C is the direc produc space H_a \otimes H_b. Shouldn't this be considered a postulate? or it is a logical consecuence of something more...

I'm still undergraduate and want to explore various branches of physics. I just feel that I like theory more and that's it. However I'm curious which branch of theoretical physics allows you to explore fundamental aspects of universe. I've heard that String Theory, QG, HEP etc. only sound sexy...

Can anyone explain why the Fundamental Theorem of Algebra and the Fundamental Theorem of Calculus are called "Fundamental"? The algebra theorem states that every non-constant single-variable polynomial with complex coefficients has at least one complex root. The calculus theorem states that an...

Use the Fundamental Theorem of Calculus to find the derivative of the function g(x) = \sqrt{x}\int sinx Ln(t) \frac{cos(t)}{t} dt g'(x) = lnx cosx / x. By integrating this function, you receive the function g(x). Then by differentiating g(x) you receive g'(x) which is what is...

Hi, I'm very new to special relativity and have a very basic question. A and B are moving from each other at a speed of v at some instant a light flashes in the space. A records: At time t a light flashed at x B records: At time t' a light flashed at x' Here is what I...

What's the minimum number of objects required for a force to be present? I assume it's 2, because you'd need one object to be moved and the other to apply the force. Is this correct? Thanks

Could electrons be non-fundamental particles. What if electrons are made of other matter particles. Could these particles interact with each other and exist but had not been given much thought about its existence because the electron alone explains much phenomena except wave-particle Duality...

I'm graduating with a B.S. in physics and I will soon be starting a Ph.D. program in nanoscale science, which is essentially an applied physics program. I chose this program because my undergraduate research was focused in this area and I've really enjoyed it. However, I'm wondering if my...

Is energy more fundamental than time or vice versa? Is Momentum more fundamental than position or vice versa? Is the quantization of energy, more fundamental than the quantization of charge, or vice versa?

Alright I've been going crazy with this problem. I'm building an electrostatic loudspeaker. In order to get it right I need to find the Fundamental frequency of the vibrating membrane. This membrane will be of an elastic substance, Mylar. Approx. 5 microns think with a young's modulus of about...

The usual perception is quantum field theory is not fundamental since it has divergence. A fundamental theory must always be finite, like string theory. But in the physical sense, a fundamental theory means it is valid at any arbitrary energy scale. We know that non-renormalizable theories...

gravity: Fg = GM1M2/r^2 electro-magnetic: weak force: strong force:

So, the area under a curve is determined by F(b) - F(a), how does that take into account the changing area between the two extremes, a and b? I mean, since F(b) and F(a) are specific values at the ends of the graph, how is the area in between figured into it, especially if the graph is really...

Homework Statement A harpsichord string of length 1.60 m and linear mass density 25.0 mg/m vibrates at a (fundamental) frequency of 450.0 Hz. (a) What is the speed of the transverse string waves? (b) What is the tension? (c) What are the wavelength and frequency of the sound wave in air...

Is there something in string theory that requires strings to be the most fundamental structure?

Does the Fundamental Theorum of Algebra prove that imaginery numbers have to exist for our number system to be complete?

Fundamental Frequency! [SOLVED] A nylon string is stretched between fixed supports 0.75m apart. Experimental plucking of the string shows that several standing waves can exist on the string. Two such standing waves have frequencies of 225Hz and 300Hz with no other frequencies in between. Q1...

I'm an Electronic and communication Engineer, and I'm living in the Caribbean, and i want to study MSc in Quantum Fields and Fundamental Forces Imperial College London, since in its description seems very likely what I'm looking for, which is,... I'm looking a course that can place me in...

This is not important, but it's been bugging me for a while. I'm struggling to see how the locally constant sheaves of vector spaces on X give rise to representations of the fundamental group of X. The approach I've been thinking of is the following. Given a locally constant sheaf F on X...

We used to think gravity and electromagnetism were the two fundamental forces of nature until we discovered the strong and weak nuclear forces. Can we be wrong again and discover more forces. If not, then how are we so sure?

Now this might seem to be a very stupid question. But neverthless, I don't understand why the fundamental quantization of energy must be hv? why not any value lower or higher like hv^2 or h/v^2. Is it possible to prove that this value of quantization is most favourable than any other value...

What are the fundamental base units for Force and Volume? I think its cm3 for volume but not completely sure.

Is the second law of thermodynamics fundamental? Like Newton's laws for example. I'm having doubts about the increase of entropy of any system. Poincaré stated the recurrence theorem which goes against the increase of entropy of a dynamical system with respect to time. By this theorem, a...

What are the odds that any particular big bang will result in the 20(?) fundamental parameters having the values that will allow life to form?

The "Strand Model" of fundamental interactions [Mentor's note: This thread is a consolidation of three different threads which were started in our Beyond the Standard Model forum. They were moved to our former Independent Research forum, because in our view this represents a "new" or "personal"...

Sources say if lines are parallel they will repel else try and merge which I don't agree and even see practically. Suppose we have 2 opposite charges facing each other, the lines are parallel, they should repel. Similarly if 2 equal charges are facing each other, the direction of the lines...

Homework Statement A stretched wire vibrates in its fundamental mode at a frequency of 384 Hz. What would be the fundamental frequency if the wire were half as long, its diameter were doubled, and its tension were increased five-fold? Homework Equations F=...

Homework Statement If G is a finite abelian group that has one subgroup of order d for every divisor d of the order of G. Prove that G is cyclic. Homework Equations The Attempt at a Solution

When one compares the fundamental solution for Laplace's Equation one might note that in 2 dimensions this solution becomes unbounded as r goes to infinity while in 3 dimensions the solution goes to zero as r goes to infinity. Now I understand both mathematical derivations so my question is...

Homework Statement A tube closed at one end and open at the other has a fundamental frequency of 242 Hz. What is the fundamental whenboth are open? Homework Equations f (open and closed) = v/4L f (open) = v/2L v sound = 343 m/s The Attempt at a Solution f1 (open and closed) =...

One of the harmonics on a string 1.4 meters long has a frequency of 18.4 Hz. The next higher harmonic frequency is 23.9 Hz. (a) What is the fundamental frequency of the string? f1 = Hz * 5.5 OK (b) What is the speed of the waves on the string? v = m/sec the...

Homework Statement A guitar string is 90.0 cm long and has a mass of 3.17 g. From the bridge to the support post is 60.0 cm and the string is under a tension of 506 N. What are the frequencies of the fundamental and first two overtones? (f1,f2,f3) Homework Equations v=sqrt(FT/m/l)...

Homework Statement Find a function f : [-1,1] ---> R such that f satisfies the following properties: a) f is continuous b) f is restricted to (-1,1) is differentiable c) its derivative f' is not differentiable on (-1,1) Homework Equations The Attempt at a Solution I kinda...

The filament of a bulb when it gets heated to some threshold level generates the visible light. My query: 1. Why is it called electromagnetic then? Here, if i understand correctly, the waves are produced by the energy emitted by the transition of the electrons between various orbits of the...