## Illinois pipeline map

Notice that by changing the coefficient of the function, we control its scaling factor— a vertical stretch or vertical shrink of the basic sine curve. We call this the amplitude of the curve — the height of the curve above its axis of symmetry. The amplitude of y = a sin x ory = acosx is the largest value of y and is given by lal.

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Amplitude, frequency, wavenumber, and phase shift are properties of waves that govern their physical behavior. Each describes a separate parameter in the most general solution of the wave equation. Together, these properties account for a wide range of phenomena such as loudness, color, pitch, diffraction, and interference. Waves propagating in some physical quantity ... Then, graph the function and identify its period. Y — sin 4x Writing f(x) = a sin—x or f(x) = a cos} Explain 2 You can write the equation of a trigonometric function if you are given its graph. Write an equation for each graph. Because the graphk y-intercept is 0, the graph is a sine function. Since the maximum and minimum values are 2 and

The average of a cosine squared function over a period is one-half the maximum so in this case the average intensity is proportional to $\frac 12 \times 4A^2 = 2A^2$. So all that is happening is that the energy is being channel along preferred directions rather that travelling uniformly in all directions.