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A sound wave is modeled with the equation y = 1/4 cos 2 pi/3 theta

AFind the period. Explain your method.
BFind the amplitude. Explain your method.
CWhat is the equation of the midline? What does it represent?

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Verified Answer :

\(y=A \cos(Bx)\)
A - amplitude
\(\frac{2\pi}{B}\) - period

\(y = \frac{ 1 }{ 4 } \cos \frac{ 2\pi }{ 3 } \Theta\)

1. A = \(\frac{1}{4}\)
2. \(\frac{2\pi}{B}=\frac{2\pi}{\frac{2\pi}{3}}= \frac{\frac{2\pi}{1}}{\frac{2\pi}{3}}= \frac{3\times2\pi}{1\times2\pi}=3\)
3. Since nothing is added or subtracted outside, the "midline" is the x axis y = 0

onyebuchinnaji

(a) The period of the sound wave is 3.0 s

(b) The amplitude of the sound wave is 1/4

(c) The equation of the midline represents x-axis.

Period of the sound wave

The period of the sound wave is calculated as follows;

y = A cos(ωt)

where;

  • A is amplitude of the sound wave
  • ω is angular speed

y = A cos(2π/T)

2π/T = 2π/3

T = 3

Amplitude of the wave

A = 1/4

The middle of the equation is on x - axis

Learn more about amplitude of waves here: https://brainly.com/question/19036728

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