Equation For Sine Wave Math

Where a b c and d are constants.

Equation for sine wave math. 2 sin 4 x 0 5 3 amplitude a 2 period 2π b 2π 4 π 2 phase shift 0 5 or 0 5 to the right vertical shift d 3. 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. A wave function is any function such that f x t f x vt. If the period is more than 2π then b is a fraction.

As we saw earlier the basic formula representing the sine function is. On the mathematics of the sine wave y x a 2πft ø why the understanding the sine wave is important for computer musicians the sine wave is mathematically a very simple curve and a very simple graph and thus is computationally easy to generate using any form of computing from the era of punch cards to the current era of microprocessors. For reference a 2d sine wave would be of form y sin x and a 3d sine wave would be of form z sin x 2 y 2. Y sin x in this formula y is the value on the y axis obtained when one carries out the function sin x for points on the x axis.

Later in this chapter we will see that it is a solution to the linear wave equation. This results in the graph of the basic sine wave. Find the period of the function which is the horizontal distance for the function to repeat. The formula for the sine wave is a amplitude of the wave ω the angular frequency specifies how many oscillations occur in a unit time interval in radians per second φ the phase t.

The general form of the sine function is. Find the amplitude which is half the distance between the maximum and minimum. Use the formula period 2π b to find the exact value. Note that y x t acos kx ωt ϕ works equally well because it corresponds to a different phase shift ϕ ϕ π 2.

Y a sin b x c d.