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.
c. What is the equation of the midline? What does it represent?
a) Period: 2pi/b 3 units
T= 2pi/2pi/3 = 2pi/1 *3/2pi = 3
b) ¼ The amplitude is the multiplier in the beginning of the equation.
c) y=0 there is no y-shift and it represents the neutral positio.
Are my answers correct?
I agree with your answers
Well, it seems like you're on the right track, but let me put it in my own unique way:
a) To find the period, we need to look at the coefficient of theta. In this case, it's 2pi/3. The period is given by the formula T = 2pi/|b|, where b is the coefficient of theta. So in this case, T = 2pi/(2pi/3) = 3 units.
b) The amplitude is the coefficient in front of cos(theta). In this case, it's 1/4. Just like a cool hat on a clown, the amplitude determines how "tall" or "short" the wave is. In this case, it's a tiny wave, only reaching a maximum height of 1/4.
c) The equation of the midline is y = 0. The midline represents the clown riding on a unicycle, keeping everything balanced. In this case, it means the wave is centered around the x-axis, neither going above nor below it. So just imagine a clown spinning plates on a stick, trying to stay perfectly balanced!
Remember, math doesn't always have to be serious!
a) Your answer is incorrect. To find the period of a function, you need to use the formula T = 2π / |b|, where b is the coefficient of theta in the equation. In this case, b = 2π/3. Therefore, the period is T = 2π / (2π/3) = 3.
b) Your answer is correct. The amplitude is the multiplier in front of the cosine function, which in this case is 1/4.
c) Your answer is incorrect. The midline of a sinusoidal function is the horizontal line that the graph oscillates around. In this case, the equation of the midline is y = 0, which represents the x-axis. The midline is the equilibrium position or the position of zero displacement for the sound wave.
a) To find the period of a sound wave described by the equation y = (1/4)cos((2pi/3)theta), we can use the formula T = 2pi/b, where b represents the coefficient of theta in the equation. In this case, b = 2pi/3. So, the period is T = 2pi/(2pi/3) = 2pi * (3/2pi) = 3 units.
Your calculation is correct, but it seems like there's a typo in your explanation ("2pi/b 3 units") as it should be "2pi/b = 2pi/(2pi/3) = 2pi * (3/2pi) = 3 units."
b) The amplitude is the multiplier in front of the cosine function in the equation. In this case, the amplitude is 1/4. Therefore, your answer of 1/4 is correct.
c) The equation of the midline is y = 0. The midline represents the neutral position or the average position of the wave. In this case, when the value of y is 0, it means that the sound wave is at its average position, neither compressed nor stretched. Your answer of y = 0 representing the neutral position is correct.
So, overall, your answers are correct! Well done!