Sine Wave Equation Math

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Sine wave equation math. In mathematics the sine is a trigonometric function of an angle. U t x a sin k x ω t φ displaystyle u t x a sin kx omega t varphi when two waves having the same amplitude and frequency and traveling in opposite directions superpose each other then a standing wave pattern is created. The mathematical equation representing the simplest wave looks like this. I recently learned that an audio sine wave is called that way because it is of the shape of the graph of a sine function.

Sin x is the default off the shelf sine wave that indeed takes pi units of time from 0 to max to 0 or 2 pi for a complete cycle sin 2x is a wave that moves twice as fast sin x 2 is a wave that moves twice as slow so we use sin n x to get a sine wave cycling as fast as we need. Thanks for contributing an answer to mathematics stack exchange. So go easy. The sine of an acute angle is defined in the context of a right triangle.

Sine waves traveling in two directions in space can be represented as. Y sin x this equation describes how a wave would be plotted on a graph stating that y the value of the vertical coordinate on the graph is a function of the sine of the number x the horizontal coordinate. Back them up with references or personal experience. Find the period of the function which is the horizontal distance for the function to repeat.

If the period is more than 2π then b is a fraction. Use the formula period 2π b to find the exact value. To find the equation of sine waves given the graph. But avoid asking for help clarification or responding to other answers.

Use mathjax to format equations. The general form of the sine function is y a sin b x c d where a b c and d are constants. For the specified angle it is the ratio of the length of the side that is opposite that angle to the length of the longest side of the triangle the hypotenuse. Guitar player and programmer here don t know much about math.

To be able to graph a sine equation in general form we need to first understand how each of the constants affects the original graph of y sin x as shown above. Find the amplitude which is half the distance between the maximum and minimum.