Question

the middle - note c has a frequency of 262 hertz and can be modeled using a sine function with an amplitude of 1.5, where x is time in seconds. which function represents the vibrations of this note? y = 1/2 sin(262πx) y = 3/2 sin(524πx) y = 3sin(262πx) y = 3sin(524πx)

Explanation:

Step1: Recall sine - wave formula

The general form of a sine - wave function for a periodic phenomenon is $y = A\sin(Bx)$, where $A$ is the amplitude and $B = 2\pi f$ ( $f$ is the frequency).

Step2: Identify the amplitude

Given that the amplitude $A = 1.5=\frac{3}{2}$.

Step3: Identify the frequency and find $B$

The frequency $f = 262$ hertz. Then $B=2\pi f=2\pi\times262 = 524\pi$.

Step4: Write the sine - function

Substitute $A=\frac{3}{2}$ and $B = 524\pi$ into $y = A\sin(Bx)$, we get $y=\frac{3}{2}\sin(524\pi x)$.

Answer:

$y=\frac{3}{2}\sin(524\pi x)$ (the second option in the multiple - choice list you provided, although the formatting in the list seems a bit off in the original image)