Formula Definition and 1000 Threads

I am desperate. I've scoured the web for the formula for the probability density function for the interference pattern obtained in the double slit experiment with both slits open. So I want to know the probability density function and not the intensity function. I prefer not to have references...

Recently, I have been playing with polarisation microscopy and the measuring of elliptical polarisation. Standard treatments, like that in Born and Wolf, are usually a mayhem of all kinds of trigonometric functions. Now I derived a nice relation, which I didn't find in literature, although I am...

I am trying to follow the solution to the following problem, both linked in the attachment. When trying to find the acceleration, a, that should be taking the derivative of r, the position formula twice. When doing so I get v = -ksinθ and a = -kcosθ. The attached work shows v being -(ksinθ)θ'...

1.) In electromagnetics, wavelength in a medium is $$\lambda = \frac{\lambda_{0}}{n}$$, where $$n$$ is the refractive index. What is the equivalent formula for sound wave in a medium? 2.) Is there a reference sound velocity, like electromagetic wave speed in vacuum is $$c_{0} =...

I know the v = λf is the formula to find the resonance frequency of a single continuous wave and the formula for resonance frequency of a spring is: 1/2π∗sqrt(𝑘/𝑚) but what about the Formula for a random object? a car, or a rock, water ? is there one Formula to rule them all? or do you...

Trying to calculate a circumference of a sphere from a radius of 3.09 inches. Is 19.4 a correct answer? Just ran numbers in the first circumference calculator I found http://calcurator.org/circumference-calculator/. Can I use the same formula for a sphere? What can I say ...Geometry is not my...

Hi, I have a formula which I need to rearrange but it's been a while since I covered this at school, I've tried to read up and re-study but I keep getting confused about what I can/can't do to the various brackets. The formula is: M = (((W x L / 2) x (L / 2)) - ((W x L / 2) x (L / 4))) I'm...

Standard formula for final velocities ##v_1##, ##v_2## in elastic collision with masses ##m_1##, ##m_2## and initial velocities ##u_1##, ##u_2## is given by $$v_1 = \frac{m_1-m_2}{m_1+m_2}u_1+\frac{2m_2}{m_1+m_2}u_2$$$$v_2 = \frac{2m_1}{m_1+m_2}u_1+\frac{m_2-m_1}{m_1+m_2}u_2$$. By rearranging...

In my textbook on EM, the formula for self inductance of a finite solenoid is given as: L= (μ(o)* N^2*A * {√(a^2+ l^2) - a} )/l^2 where a=Radius of each turn, l=length of solenoid. I am having trouble and extreme difficulty in trying to ascertain how this formula was derived in the book and...

Hello, I normally get these things working but I am a bit stuck as i don't feel I am getting sensible answers... The problem is simple (!): Q: Model the flow through an orifice with an upstream/supply pressure of 301BarA where the downstream pressure is in the range 1BarA to 301BarA. The...

Variance and standard deviation and other measures of error I understand. This formula doesn't behave well for data sets centered around zero and also has other problems, like scaling differently as N increases than the standard deviation or standard error. Does anyone recognize this and can...

Hello, I am trying to solve a problem and I would like to ask for help. I have 3 points (A, B, C) in 3D space that are assumed to be on a circle. EXAMPLE 1 EXAMPLE 2 My goal is to create an algebraic formula to calculate the coordinates for 10 points on a circle composed of ABC points at...

In two different textbooks, there are two different formulas with different derivation styles for the "No Fringe Formation" Condition. In approach (a), they use an amalgamation of bright and dark for 2 wavelengths having very minute difference in the following manner: 2dcostheta=n*λ(1)...

I think that it is a trick question and that the answer is that given dependence does not exist. Could anyone tell me if I am right?

Is the following molecular formula for Sugar can be written as H22C12O11 or O11C12H22 or O11H22C12 or C12O11H22 or H22O11C12 instead of C12H22O11? Logically they can be written as mentioned above? If Not, Why? There can be many more examples similar to above.

I want to ask several questions regarding to the text: 1) Why do we find the minima of the diffraction? Why not the maxima?2) "Figure 25.32b shows two rays that represent the propagation of two wavelets: one from the top edge of the slit and one from exactly halfway down" Why do we take point...

Consider that the particle is moving in circular with tangential velocity v, and (0,0)is its origin. I wonder why dr/dt is equal to tangential velocity instead of radial velocity (since dr/dt means how much change in radial distance in a really short duration of time)

i spoke to my proffesor about it but all he said was to put 1 in m1 and m2... for r^2 since it says to quadruple to just put 4^2 I asked about the G in the equation but he said not to worry about iit and pretend its not there...

If the wire is bent by three pivots, I want to find an expression that represents its shape. There will be tension of wire and other physical factors. How can it be expressed?

Hello I am reviewing the proof of Cauchy's formula for the stress tensor and surface traction. Without exception, every book I look at gets to the critical point of USING the projection of a triangle onto one of the three orthogonal planes. However, I have never seen this proven. I have...

I believe I have understood the formula of aberration of light ##\tan \theta' = \dfrac{\sin \theta}{\beta + \cos \theta} \sqrt{1-\beta^{2}} ## but I wonder if the non-relativistic formula ## \tan \theta' = \dfrac{\sin \theta}{\beta + \cos \theta} ## has a physical relevance. Does this...

Can somebody please derive for me an example of the Binding energy from the Semi Empirical mass formula? I am trying myself but always there is a difference between the database binding energy and my own result. I am calculating the BE of Niobium 93. For the mass formula I used the coefficients...

Hi all, I was thinking punching a round ball on a flat surface and seeing how I could determine a formula for force from it. I thought the following: 1. The ball will go further the harder I punch and thus force must be proportional to displacement d. 2. Ball will go further if it is lighter...

I have spent years physically charging high pressure bottles with multi staged bicycle pumps and spent large sums of money on electric high pressure air pumps not unlike a scuba tank air compressor. Pressure’s can be as high as 4500 PSI . The pressurized bottles are usually 300 to 500 cc’s. I...

While fighting a CAD program, today, I might have stumbled on a potential way to easily calculate the circumference of an ellipse. I checked my method against a half a dozen online ellipse calculators and while my formula gives different results, I can't see where I'm making any logical errors...

Red arrows. The notes initially say that the error term is positive. After substitution of A and C which are clearly positive, the term suddenly became negative...? Is this a typo, or is there a theory behind this?

There are actually several questions. The formula for calculating the "beam angle" of light (emitted from lights bulbs, flashlights etc) is - α = 2 arcCos ( 1 - Lm ÷ ( 2 π Cd )) Where, α = beam angle in degrees Lm = luminous flux (Lumens) Cd = luminous intensity (Candela) The above formula...

Dear colleagues, I am dealing with rope friction and the so-called Capstan equation. Situation: A rope wraps around a cylinder with a wrap angle. It depends on the input force. There are very comprehensive approaches by other colleagues, where the friction value depends on the normal force or...

In many cases, the concentrations of defects or charges are quite big enough to use SA, due to a big number of Avogadro's number. The derivation for the well-known formula of a defect concentration is followed. If the n_v is expected to be lower than 1, then it would be impossible to use SA...

A 4×3 matrix which has all elements empty, now I select any two consecutive elements until all elements are selected. I assign an index number (1 to 12) to the matrix element, in one row there are only 1,2,3 elements and 3 & 4 are not consecutive. for example, if I select index 1 & 2 of the...

In "Gravitational radiation from point masses", by Peters & Mathews, http://gravity.psu.edu/numrel/jclub/jc/Peters_Mathews_PR_131_435_1963.pdf, the emitted power from gravitatioanal quadrupole radiation per unit solid angle ##\Omega## is given by: $$ \frac{dP}{d\Omega} = = \frac{ G} {8 \pi c^2...

Just as the time dilation formula for the Schwarzschild metric in terms of the position ##r## away from center of mass for a gravitational body and the Schwarzschild radius ##r_s = {2GM}/{c^2}## is given by $$ \tau = t \sqrt{1 - \frac{r_s}{r} } $$ so I'd like to know the corresponding...

Hello, I have been thinking of it for a long time, and I would appreciate suggestions from math experts. I am working on a simulation of human agents. I want to set up a formula that defines the consumption probability (0,1), which consists of X, a value between 0 and 1, and two positive and...

I want to find a formula for an action potential (illustrated with the curve in the attachment). I would like to use the formula to graph this in Desmos graphics calculator. I don't have much of a math background, but a sine function comes to mind...I would like to get the precise shape though...

I haven't gone into a solution cause I found this question confusing

This is exercise 12.1.2 a from Arfken's Mathematical Methods for Physicists 7th edition :Starting from the Laguerre ODE, $$xy''+(1-x)y'+\lambda y =0$$ obtain the Rodrigues formula for its polynomial solutions $$L_n (x)$$ According to Arfken (equation 12.9 ,chapter 12) the Rodrigues formula...

Why is ##E = \int (\vec v \times \vec B) \cdot d \vec l##? This seems to be a general formula, and I would like to know its proof. Thanks for all the help.

It is an electron initially pushed by the action of the electric field. The vectors of force and velocity are parallel to each other. Here's the questionA possible expression of speed as a function of time is the following: $$v(t) = \frac{At}{\sqrt{1 + (\frac{At}{c})^2}}$$where is it $$A...

It is an electron initially pushed by the action of the electric field. The vectors of force and velocity are parallel to each other. Here's the questionA possible expression of speed as a function of time is the following: $$v(t) = \frac{At}{\sqrt{1 + (\frac{At}{c})^2}}$$where is it $$A...

For ##\hat{S}^+## and ##\hat{S}^{-}## operators for any given spin ##S## relation \hat{S}^+|S,m \rangle=\sqrt{S(S+1)-m(m+1)}\hbar|S,m+1 \rangle \hat{S}^-|S,m \rangle=\sqrt{S(S+1)-m(m-1)}\hbar|S,m-1 \rangle Can someone please explain how we get those factors ##\sqrt{S(S+1)-m(m+1)}\hbar## and...

The question is below. I tried reasoning that because x is constant, E is also constant however that gives me values in the range of 10^51. Then I tried to use numpy's ivp_solve function to solve the differential equation however I wasn't able to get that working either. Apparently I'm meant to...

According to the equation, the answer is B. Since the lecture didn't cover much about it, can someone explain this formula in a less physics way? Thanks.

My mentor wants the derivation of this formula. Me a computer undergrad, unable to figure it out, and my final project are on a halt due to this, any help from the community is greatly appreciated!

I have no idea how to do this. I've tried conservation of mechanical energy and it didn't work. Ek = Kinetic Energy R = horizontal range of the ball h = height from which the ball is released

A bag has identical balls of these colors: 1 white, 6 red, 9 green, and 3 purple. Without looking, a ball is drawn from the bag. You would most likely get a a. green ball b. purple ball c. red ball d. white ball

I think it has to do with conversation of momentum and projectile motion.

Hello. I am reading through a solar farm paper and I am getting a bit confused at looking at this formula: When it says "Value", I am guessing it refers to the cost of electricity per kWh? If that is the case, I wonder how many kWh are 18.4p/kWh?

Here is a simple way to get Euler's relation for those learning pre-calculus/calculus, so the trigonometric addition formula and the derivative of sine and cosine are easy. We will assume some basic knowledge of complex numbers and properties of Euler's number, e. Consider a small segment of...

Hello! I'm having trouble with getting the right result in this litle example. Consider this admittance $$ C + Cs - w^2_{pr} CCs $$ Now to get the resonance we need to set the imaginary part of the admittance 0.I did that like this $$0 = C + Cs - w^2_{pr} CCs $$ Now I need to get ## w^2 ##...