Fundamental Definition and 907 Threads

How do we show that the fundamental group of the disk D^2={(x,y) in RxR: x^2 +y^2< or eq. to 1} is trivial? I know how to show that the fundamental group of the circle is isomorphic to the group of the integers under addition, but for some reason, I don't see a way to show that the...

A convincing way to reason inverse square law (of classical EM and gravity) is a conservation of the field lines as one proceeds away from a source... http://hyperphysics.phy-astr.gsu.edu/HBASE/forces/isq.html It appears as a reasonable and intuitive thing to expect... but, it does NOT seem...

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...

in Thermodynamics, in a book i have read that during expansion of a gas(system), W(on system by surroundings)=-ve..They have proved it using W=-force(external)*displacement. They are saying as displacement is positive and force is always considered as positive, W=-ve. But, how did they determine...

Homework Statement Can y = sin(t^2) be a solution on an interval containing t = 0 of an equation y'' + p(t)y' + q(t)y = 0 with continuous coefficients? Homework Equations The Attempt at a Solution y = sin(t^2) y' = 2tcos(t^2) y'' = 2cos(t^2) - 4t^2sin(t^2) 2cos(t^2) -...

1. The problem is: A guitar string is 78 cm long and has a mass of 3.6 g. The distance from the bridge to the support post is L = 60 cm, and the string is under a tension of 505 N. What is the frequency of the fundamental? I don't get why it gives me two distances. Which one is L? 2. The...

Could some one help me understand the difference and the similarties between Coulombic fundamental force and Gravitational fundamental force?

Homework Statement A vibrating string on a violin is 330 mm long and has a fundamental frequency of 659 Hz. What is its fundamental frequency when the string is pressed against the fingerboard at a point 60 mm from its end? *The answer is 805 Hz Homework Equations f = \overline{}nv/2L...

For a second order linear differential homogeneous equation, if the two solution y1 and y2 is a multiple of one another. It means that it is linearly dependent which mean they can not form a fundamental set of solutions to second order differential homogeneous equation. Am I correct?? or...

Cells are constantly being replaced at a high rate, but why does our skin wrinkle nonetheless? When you workout or are involved in any physical activity, and you eat enough protein, muscle tissue is being built and repaired. Why do reflexes slow? It's still the same or nerve channels being...

Homework Statement The length of a string is 1440 cm. The string is held fixed at each end. The string vibrates in eight sections; i.e., the string has eight antinodes, and the string vibrates at 150 Hz. What is the fundamental frequency? Answer in units of Hz.Homework Equations f = nv / 2L...

Is it possible for a harmonic (produced by a stringed instrument) to have an amplitude higher than the fundamental. If so how?

The fundamental definition of temperature is T^{-1} = \frac{dS}{dE} How can I verify that the dimensions work in this equation?

Homework Statement A 40-cm long string, with one end clamped and the other free to move transversely, is vibrating in its fundamental standing wave mode. If the wave speed is 320 cm/s, the frequency is: A) 32 Hz B) 16 Hz C) 8 Hz D) 4 Hz E) 2 Hz Homework Equations v = \lambdaf L =...

Hi all :D, Is there such a thing as fundamental equations that are at the root of all physics? Thanks PS If yes- then please provide a link to it if possible. Thanks

This principle states that the electron starts filling from the lowest energy up. Why?

Homework Statement The question: F'(\pi/2) if F(X)= \int^{cosx}_{0} e^{t^{2}}The Attempt at a Solution I thought I thought F'(X) = f(t) = e^{t^{2}} replacing t with cos^{2}x But my book writes: F'(x) = (-sinx)e^{cos^{2}x}

Homework Statement Evaluate the following definite integrals using the Fundamental Theorem of Calculus: 1. 1 \int 4 ( (5x2+7x+5)dx ) 2. -5pi/6 \int 4pi/6 (−6sinx+7cosx) dx ) 3. 2 \int 4 ( (e^-4x)/((e^(-4x))+7) dx ) If it's unclear, the number on the...

Hi all Im trying to derive the time-harmonic form of the Maxwell equations from the original, time-dependent form, however I am not sure if my working and logic is correct e.g. for \nabla\times E = -dB/dt I want to be able to get \nabla\times \vec{E} = -j\omega\vec{B} where...

Homework Statement The FTC states that {d\over{dx}}\int_a^x f(t)dt = f(x) Now, how do I do something like {d\over{dx}}\int_a^{g(x)} f(t)dt = ?Homework Equations The Attempt at a Solution I know that it has to do with the chain rule, but I forgot my textbook at school and I can't seem to find it...

Hi.guys i have some confusion on the fundamental therom of calculus. here is my question. 1. somethimes when i use the fundamental therom of calculus which is F(a) - F(b). the out come will be negative .in the same question when i type in my calculator its only give me positive i guess is...

Homework Statement A stretched wire vibrates in its fundamental mode at a frequency of 400Hz. What would be the fundamental frequency if the wire were half as long, with twice the diameter and with four times the tension? Homework Equations fn = nV / 2L where n is the harmonics...

There are two theorems: The fundamental theorem of calculus: \int_{a}^{b}F'(x) = F(b) - F(a) And the theorem that states if f is continious on [a,b]and g:[a,b]->R is defined by g(x) = \int_{a}^{x}f(t) dt, then g is differentiable on (a,b) and; g'(x) = \frac{d}{dx}(\int^{x}_{a}f(t)) =...

Homework Statement An open organ pipe (i.e., a pipe open at both ends) of length L0 has a fundamental frequency f0. Part A If the organ pipe is cut in half, what is the new fundamental frequency? 4f0 2f0 f0 f0 f0 Part B Part C This part will be visible after you complete...

As I understand it, the sensation of smell is caused by small amounts of matter leaving the body before being incident on olfactory receivers in our nose. Now, since the 'smell' has mass and it is leaving the body, could there eventually arise a situation where some body loses all its mass as...

I have been trying this problem for a long time now. Factor the polynomial t^7+2t^6-24t^5. So far I came up with t^n(t+x)(t+y). I have no clue on how to work this out because i am only able to do them to the 2nd degree. I can really use the help. Thanks, Neil

hii i have a problem that why ampare{unit of current} is fundamental unit, ampare is I=Q/t and it is drived.while electric charge is not a drived unit and it also measured by millican mattod.and if we place coulomb{unit of electric...

Well i do understand about the 8 fundamental dimensions in physics, but i cannot understand what makes only the length, mass and time to commute with one another to produce derived units like force or acceleration. Why cannot we have a unit something like K^2 or sqrt(candella)?

http://blog.wired.com/gadgets/2008/08/bell-labs-kills.html" Six Nobel-prize worthy research came from that lab, including the invention of the silicon transistor, and the laser! It was a business decision by the parent company but, I think it's a very myopic business decision to abandon...

I've just read in the first pages of The Elegant Universe that Greene believes that all fundamental laws should be contained in the microscopic domain, all other laws are derived. Is it really so evident that the laws of thermodynamics are derived and not fundamental? The second law, is it...

Can the Schroedinger equation be derived from first principles in BCS theory? Zapperz suggests the Madelung and Schroedinger equations are not fundamental in BCS theory. If such is the case, how exactly does such a derivation work?

Homework Statement The organ pipe is 2.0 m long, was open at both ends, and was originally tuned to a fundamental frequency of 128 Hz (C below middle C). a) what is the wavelength of the fundamental? b)if the note you now hear is closer to 262 Hz (middle C), where is the blockage with...

Homework Statement Find 2 \int 0 \ (2-x^2)dx using def of the definite integral and using FTC Homework Equations The Attempt at a Solution any help on how to start would be great?

Homework Statement Question One: Find a continuous function f and a number a such that 2 + \int_{a}^{x} \frac {f(t)} {t^{6}} \,dt = 6 x^{-1} Question Two: At what value of x does the local max of f(x) occur? f(x) = \int_0^x \frac{ t^2 - 25 }{ 1+\cos^2(t)} dt The attempt at a solution I...

Homework Statement Evaluate each definite integral. ok I'm not sure how to do the integration sign, but... b=4, a=1 for (5yy^.5)+3y^.5)dy Homework Equations The Attempt at a Solution I'm not really sure what I'm doing wrong. i integrated...[tex]5y^2/2*y^(3/2)/(3/2)+3y^(3/2)/(3/2) then i...

A standing wave resonates at 400 Hz with three antinodes on a string tied tightly between two posts 2.0 meters apart. What is the wavelength of this standing wave? What is the fundamental frequency of this string? I tried to draw the picture out, and it looks like the wavelength is just...

Some Fundamental Interactions Of Matter Found To Be Fundamentally Different Than Thought ScienceDaily (July 2, 2008) — Collisions have consequences. Everyone knows that. Whether it's between trains, planes, automobiles or atoms, there are always repercussions. But while macroscale collisions...

Can somebody explain to me, geometrically and intuitively, the fundamental theorem of calculus? I understand that i can find the area between the graph of f'(x) and the x-axis where b>x>a by finding f(b)-f(a), but i don't understand why. Suppose something is too hard to integrate. Can i...

Hi, I'm extremely new to quantum mechanics (my only knowledge of quantum mechanics is that taught in physics C, ergo none, and a bit of wave mechanics... however I have a pretty strong mathematics background... diff-eqs + linear alg. + vector calc.), and was wondering as to how the derivation of...

Hi everyone, Can scientific research be founded on utility ? I expect this to be a contreversial topic. I certainly do not want to bias the answers by my own opinion. I was surprised to discover a few other researchers' opinions. Sorry if this does not belong to GD, please move to the...

Hi , i have this question - it's not an idea , and it's not a theory indeed , it's merely a question - we all know that the theory of relativity is inspired by maxwell theory of electromagnetism , from which the constancy of speed of light in any frame of reference is derived . and we know that...

how is trignometric ratios like sine theta is defined to be the ratio of perpendicular and hypotenuse in a right angled triangle?

i wondered at the idea that calculus works for continuous functions and in reality fundamental quantities are discontinuous. For example energy or an electron can't asume all values. Therefore isn't there a conflict when we work on a equation like dE/dt or something similar which involve...

I attended a colloquium a few days ago concerning the LHC and the search for the Higgs Boson. After some thought, I have the following question. Among other things, there are two measurable properties of all of the fundamental particles in the Standard Model: mass and charge. It is...

I just don't get this stuff. I've been trying on my own with the book. Also, is there a better way to post this? Homework Statement tanx 1 + secx _________ + _________ = 2csc x 1 + secx tanx I need to prove that this side equals the other. Homework...

Homework Statement A parachutist of mass 70kg, in free fall at 136 km/h, opens a parachute. if the chute creates a 895 N air resistance force and the parachutist is being pulled down by a force of gravity at 686 N a) find hte acceleration of the parachutist b) how far does she fall in 5.0 s...

Here is an interesting question that my urge for simplification and basic/fundamental understanding has lead me to ask: -------------------------------------------------------------- What would you say are the most fundamental ideas of Physics, the most fundamental science? By fundamental what...

Suppose that p and q are continuous on some open interval I and suppose that y1 and y2 are solutions o the ode y''+(t)t'+q(t)y=0 a. Suppose that y1 , y2 is a fundamental set of solutions. Prove that z1, z2 given by z1=y1+y2, z2=y1-y2 is also a fundamental set of solutions. b. prove that...

My question goes as follows: An open pipe in air is designed to produced 2 successive harmonics at 235 Hz and 275 Hz at 20 degrees Celsius. What is the fundamental frequency? What is the length of the pipe (m)? I'm not sure how to solve this problem, as I can't find the equation to...

My question goes as follows: An open pipe in air is designed to produced 2 successive harmonics at 235 Hz and 275 Hz at 20 degrees Celsius. What is the fundamental frequency? What is the length of the pipe (m)? I'm not sure how to solve this problem, as I can't find the equation to...