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A sine wave or sinusoid is a mathematical curve that describes a smooth periodic oscillation.A sine wave is a continuous wave.It is named after the function sine, of which it is the graph.It occurs often in pure and applied mathematics, as well as physics, engineering, signal processing and many other fields. Its most basic form as a function of time (t) is:


When finding the equation for a trig function, try to identify if it is a sine or cosine graph. To find the equation of sine waves given the graph, find the amplitude which is half the distance between the maximum and minimum. Next, find the period of the function which is the horizontal distance for the function to repeat.


The following diagram shows how to find the equation of a sine graph. Scroll down the page for examples and solutions. Find an Equation for the Sine or Cosine Wave When finding the equation for a trig function, try to identify if it is a sine or cosine graph. To find the equation of sine waves given the graph 1.


Amplitude, Period, Phase Shift and Frequency. Some functions (like Sine and Cosine) repeat forever and are called Periodic Functions.. The Period goes from one peak to the next (or from any point to the next matching point):. The Amplitude is the height from the center line to the peak (or to the trough). Or we can measure the height from highest to lowest points and divide that by 2.


Transformed cosine and sine curves, sometimes called wave functions, are cosine and sine curves on which we have carried-out a series of transformations. In their most general form, wave functions are defined by the equations : \[y = a.cos\begin{pmatrix}b(x-c)\end{pmatrix}+d\]


E z t A kz t A kz t( , ) cos cos( ) sin sin( ) Thus our solution to the wave equation becomes: A cos( ) = B and A sin( ) = C Instead of the unknown constants B and C, let’s use two different unknown constants, A and . We define them so that:


The main difference between the two is that cosine wave leads the sine wave by an amount of 90 degrees. A sine wave depicts a reoccurring change or motion. It is known as sine wave as it has the similar shape as the sine function, when it is plotted on a graph. The graph shows the repetition of one wave segment in a repeated manner.


Wave Equation. In determining the wave equation we use the method of partial derivative. First you know the wave equation for the wave travelling in positive x-direction from Eq. \eqref{3} which is \[y=A\cos (kx-\omega t)\]


The wave equation is an important second-order linear partial differential equation for the description of waves—as they occur in classical physics—such as mechanical waves (e.g. water waves, sound waves and seismic waves) or light waves. It arises in fields like acoustics, electromagnetics, and fluid dynamics.. Historically, the problem of a vibrating string such as that of a musical ...


In this video David shows how to determine the equation of a wave, how that equation works, and what the equation represents. If you're seeing this message, it means we're having trouble loading external resources on our website.