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?

According to the information given, the sine function is:

The standard sine function is given by:

In which:

In this problem:

Then, the equation is:

A similar problem, which also involves building a sine function according to the desired characteristics, is given at link

 f(x) = 1.5*sin(x*2*pi/0.0038s)

Step-by-step explanation:

A sine function is:

f(x) = A*sin(c*x + f)

Where A is the amplitude, we know that it is 1.5

c is a constant that depends on the frequency.

f is a phase.

As there is no mention of a phase, we can assume f = 0.

Then our function is:

f(x) = 1.5*sin(c*x)

now let's find the value of c.

We know that the frequency is 262hz.

Then the period can be calculated with the equation:

T = 1/f.

T = 1/262 Hz = 0.0038 seconds.

Now, the period of a sin function is 2*pi.

whit pi = 3.14159265358979

Then we have that:

sin(0) = sin(c*0.0038s)

sin(0) = sin(2*pi)

then:

c*0.0038s = 2*pi

c = 2*pi/0.0038s

Then the function is:

f(x) = 1.5*sin(x* 2*pi/0.0038s)

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step-by-step explanation:

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