Hi! Can someone help me solve this sound wave equation?

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Hi! Can someone help me solve this sound wave equation?

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Answer 1 · 2018-02-23T19:59:49

$p = 3$ $p=3$ $a = \frac{1}{4}$ $a=1/4$ Midline: $y = 0$ $y=0$

Explanation:

The periods of trig functions in the form of $a sin (b θ + c) + d, a cos (b θ + c) + d$ $asin(btheta+c)+d, acos(btheta+c)+d$ , is given by $p = \frac{2 π}{b}$ $p=(2pi)/b$ .

Here, $b = \frac{2 π}{3}$ $b=(2pi)/3$ and we have an equation in the form of $y = a cos (b θ + c) + d$ $y=acos(btheta+c)+d$ , so:

$p=(cancel(2pi))/((cancel(2pi))/3)=3$

The amplitude of $asin(btheta+c)+d, acos(btheta+c)+d$ is given by $a$ . Here, we see $a=1/4$ ; therefore, our amplitude is $1/4$ .

The midline is the horizontal line $y=m$ which runs straight through the middle of the graph of the trigonometric function.

$d=0$ , so our function isn't shifted up or down at all. Here, our amplitude is $1/4$ , meaning that our highest point will only be at $y=1/4$ and our lowest point will be at $y=-1/4$ .

The line which runs through the middle of this is $y=0$ , because $0$ lies right in between $-1/4$ and $1/4$ .

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Hi! Can someone help me solve this sound wave equation?

1 Answer

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