1. OOOVincentOOO

    Audio Analysis Divisor Function

    Hello, The divisor function can be written as a summation of repeating pulses with a frequency. It can be represented with the functions below: $$1) \space \sigma_{0}(x)=\sum_{\mathbb{X}=2}^{\infty} 2^{(-N)} \sum_{k=0}^{N} \binom{N}{k} e^{-i\left( \frac{\pi}{\mathbb{X}}kx \right)} $$ $$2)...
  2. J

    Finding The Equation For An Unusual Sine Wave

    Hello everyone. I made a post in another group trying to find the answer to a question about a particular sine wave, see link: https://math.stackexchange.com/questions/3383264/finding-an-expression-for-a-tricky-sine-wave Sadly despite offering a 'bounty' for it, I've not gotten very far...
  3. M

    Phasor Representation of sine wave

    I don't understand why Sine wave should be represented as a phasor, that is, as a circle with a rotating vector. Why should it be rotating at angular speed (omega)? This is an additional item that confuses me. Suppose in the picture I am assuming it is moving at some speed; if it runs at twice...
  4. OOOVincentOOO

    Wave Divisor Function

    Dear Math Forum, For quite some time (years), I have been playing around with the divisor function (counting the number of divisors for a given integer). I created a 10 slide summary in the attached presentation. Wave Divisor Function...
  5. B

    Finding minimum value of wave

    Please forgive me if this is in the wrong section of the forum, this is my first time posting here. Anyway, I am quite stuck on this problem and require a bit of help in solving it. Sorry for the low quality image, had to rescale it.
  6. L

    Laplace transform of a forced square wave

    Hi, I am working on a problem involving an initial value problem with a forced square wave. I am trying to take the laplace inverse of [e^(-(pi)s)] / [s^3+s] From what I can tell, I can't do the partial fractions method to split the denominator and it doesn't match anything in my table of...
  7. A

    Help read wave

    Help read the graph, the formula model is in the picture.
  8. M

    Derivative of Sin wave

    Hello, I am now performing Derivative of Sin wave which is Cos wave while simulating right hand circuit giving diffrent wave form please have alook.
  9. M

    integration of Sin wave

    Hello, what this mean sin integration = -cos +C as I have simulated the circuit the time period also increase why?
  10. idontknow

    Light as Wave

    If speed of light is constant \lambda v=\frac{E}{p}=\frac{\partial\phi/\partial t}{\partial\phi/\partial x} , \: \; \delta_t(\lambda v)=0=\delta_x(\lambda v) \: since \lambda v = c \phi_t ''\phi_x '-\phi_t '\frac{\partial^2 \phi}{\partial x \partial t} =0=\frac{\partial^2...
  11. M

    Trigonometry wave

    Hello, We know Sin Wave is like this but what will be Sin² wave?
  12. M

    sine wave and sin function

    Hello, What is difference in sin wave and sin function?
  13. D

    applying wave equation to a dataset

    This may be the wrong place, since this isn't a college calc problem, so apologies in advance. I've got a set of data that evolves in a way that looks like it could be described by some form of the wave equation, but my calculus skills aren't up to the task (yet). Here's a crude animation...
  14. R

    Wave Theory of Numbers: concept of waves and remainders

    concept of waves and remainder Euclid division lemma it say's that a=b*q+r r could also be writtern as a mod q = r what it really means in wave theory is that wave if a mod q=0 , it means wave q has entered the point a (here a is considered as a point but actually it is a number)...
  15. R

    Wave Theory of Numbers: introduction

    why wave theory of numbers is needed Mathematicians have not solved questions like Oppermann's conjecture, the Riemann Hypothesis, Levy's Conjecture, Brocard's problem,the Twin Prime Conjecture and many more. To solve these questions, I build Wave Theory of Numbers(WTN), actually the theory of...
  16. D

    What is the equation of the wave in the attachment

    Some sin wave modification I think...The important points are (0,3.2) , (72,8 ) , (288,0) The point where it crosses the y axis at (0,3.2) is an inversion point (like (0,0) on the normal sin wave) Imagine the graph continues in both directions along the x axis Thanks, DarkLink
  17. M

    pde ivp 2nd order wave equation

    The analytical solution for this equation (∂^2 U)/(∂t^2 )+(∂^2 U)/∂t∂x-2 (∂^2 U)/(∂x^2 )=0 U(x,0)={(1-sin(x)x,|x|<1 0 otherwise) Assuming sin(x) =-1, x<0, 1, x>0 〖∂U/∂t〗_(t=0)={(cos(πx),|x│<1 0 otherwise)
  18. M

    I need help with this IVP wave equation

    The analytical solution for this equation (∂^2 U)/(∂t^2 )+(∂^2 U)/∂t∂x-2 (∂^2 U)/(∂x^2 )=0 U(x,0)={(1-sin(x)x,|x|<1 0 otherwise) Assuming sin(x) =-1, x<0, 1, x>0 〖∂U/∂t〗_(t=0)={(cos(πx),|x│<1 0...
  19. M

    interpreting wave equation using mathematica

    hi can someone please help me solving this problem: Let u(x, t) be a solution of a wave equation u_tt − u_xx = 0, x ∈ (0, 2π), t > 0 satisfying Neumann boundary conditions u_x(0, t) = u_x(2π, t) = 0, t > 0 and initial conditions u(x, 0) = g(x), u_t(x, 0) = h(x). Choose function g(x) and...
  20. C

    Sine wave polynomial

    Given $(n+1)$ points in the Cartesian plane, you can form a degree $n$ polynomial whose graph passes through all n points. Suppose the $(n+1)$ points are $(a_{0},\sin(a_{0})), (a_{1},\sin(a_{1}))..., (a_{n},\sin(a_{n}))$, with the $a_{i}$ in increasing order. If this polynomial is...