A sound wave is modeled with the equation y= 1/4 cos2pi/3 theta.
a. Find the period. Explain your method.
b. Find the amplitude. Explain your method.
i think the period is 2pi/3 but i feel like im wrong so could someone solve this and explain it for me? tysm.
wrong on the period
Recall that the period of cos(kθ) is 2π/k
The amplitude of cosθ is 1
So, the amplitude of A*cosθ is A*1 = A
I'm sure your book explained this as well ...
To find the period of a sound wave modeled by the equation y = (1/4)cos((2π/3)θ), we need to understand the relationship between the equation and the period of a cosine function.
a. To find the period, we need to examine the coefficient of theta (θ) in the equation. The general form of a cosine function is y = A*cos(Bθ), where A represents the amplitude and B represents the frequency.
In this case, the coefficient of theta (θ) is (2π/3). To find the period, we need to calculate 2π divided by the absolute value of (2π/3):
Period = 2π / |2π/3|
Simplifying this expression, we get:
Period = 2π * 3/2π = 3
Therefore, the period of the sound wave is 3.
To explain the method:
1. Start with the equation: y = (1/4)cos((2π/3)θ)
2. Identify the coefficient of theta, which is (2π/3).
3. Use the formula Period = 2π / |(coefficient of theta)| to find the period.
4. Substitute the coefficient of theta into the formula and simplify the expression.
5. The resulting value represents the period of the sound wave.
b. To find the amplitude of the sound wave modeled by the equation y = (1/4)cos((2π/3)θ), we need to examine the coefficient of the cosine function, which is (1/4).
The amplitude of a cosine function is the absolute value of the coefficient in front of the cosine term. In this case, the coefficient is (1/4), so the amplitude is:
Amplitude = |1/4|
Therefore, the amplitude of the sound wave is 1/4.
To explain the method:
1. Start with the equation: y = (1/4)cos((2π/3)θ)
2. Find the coefficient in front of the cosine term, which is (1/4).
3. Take the absolute value of the coefficient to find the amplitude.
4. The resulting value represents the amplitude of the sound wave.