Question

the musical 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 = 1.5 sin(262x) y = 1.5 sin(2π262x) y = 1.5 sin(262πx) y = 1.5 sin(524πx)

Explanation:

Step1: Recall the general form of a sine - wave function

The general form of a sine - wave function for a periodic phenomenon is $y = A\sin(2\pi fx)$, where $A$ is the amplitude, $f$ is the frequency, and $x$ is the independent variable (in this case, time).

Step2: Identify the given values

We are given that the amplitude $A = 1.5$ and the frequency $f=262$ hertz.

Step3: Substitute the values into the general form

Substituting $A = 1.5$ and $f = 262$ into $y = A\sin(2\pi fx)$, we get $y=1.5\sin(2\pi\times262x)=1.5\sin(524\pi x)$.

Answer:

$y = 1.5\sin(524\pi x)$