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A sound wave is modeled with the equation y= 1/4 cos (2π)/3 θ

A) Find the period. Explain your method
B) find the amplitude. Explain your method

the period of cos(kx) is 2π/k

the amplitude of A cos(x) is just |A|

Did you know?

Did you know that a sound wave can be mathematically modeled using an equation? For example, in the equation y = 1/4 cos (2π/3)θ, the letter θ represents time. A) To find the period of the sound wave, we need to identify the value that determines how long it takes for the wave to complete one full cycle. In this equation, the value inside the cosine function, 2π/3, is responsible for this. The period is given by the formula T = 2π/ω, where ω is the coefficient of θ. Therefore, in this case, the period is T = 2π/(2π/3) = 3. So, the sound wave represented by this equation completes one full cycle every 3 units of time. B) The amplitude of a sound wave determines its maximum displacement from the equilibrium position. In this equation, the coefficient in front of the cosine function, 1/4, represents the amplitude. Therefore, the amplitude of this sound wave is 1/4.