A sound wave is modeled with the equation . y=1/4cos 2pi/3treta
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- The period can not be found because there is no time in the equation.
B- Amplitude will be 1/4. I don't know exactly how to explain it...
C- I don't know about c , I need help
yeah but I can't type "Ø" unless i copy and paste it , Thanks though
c. To find the equation of the midline, we need to determine the average value or the mean of the given equation. In this case, the average value is zero because the equation is a cosine function and cos(0) = 1.
Therefore, the equation of the midline is y = 0. The midline represents the equilibrium or zero level of the sound wave. It is the horizontal line that the wave oscillates around. Any displacement above the midline represents a compression or crest of the sound wave, while any displacement below the midline represents a rarefaction or trough of the sound wave.
c. To find the equation of the midline, we need to understand what it represents. The midline is the horizontal line that the graph of the waveform oscillates around. It essentially represents the average value of the waveform.
In the equation y = 1/4*cos(2π/3*t), the amplitude is 1/4. The amplitude is the maximum displacement of the waveform from the midline. Since the cosine function oscillates between -1 and 1, the amplitude in this case tells us that the maximum value the waveform reaches is 1/4.
To find the equation of the midline, we need to find the average value between the highest point and the lowest point the waveform reaches. In this case, since the amplitude is 1/4, the highest point is 1/4 and the lowest point is -1/4. The average of these values is 0.
Therefore, the equation of the midline is y = 0. This represents the horizontal line that the waveform oscillates around.
You should find the standard form of a cosine curve in your text or in your notes.
for y = a cos (kØ) ,
the amplitude is |a| and
the period is 2π/k in radians or 360°/k in degrees
so you have y = (1/4)cos (2π/3 Ø)
your amplitude is correct
period = 2π/(2π/3)
= 2π(3/(2π)) = 3 radians
I will assume that by the "midline" you mean the Ø axis.
You should really study and memorize the basic cosine curve.