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?

Answer 1

Answer:

y=3/2 sin (524πx) or B

Step-by-step explanation:

The question tells you that that the frequency is 262 so you plug 262 in for F so you get 262 =  IBI/2π and once you solve for B you get 524π and you plug that in for B. also the amplitude is 1.5 and 1.5 is the same thing as 3/2.

Answer 2

Answer:  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)