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)
According to the information given, the sine function is:
[tex]y = 1.5\sin{(524\pi x)}[/tex]
The standard sine function is given by:
[tex]y = A\sin{(2\pi fx)}[/tex]
In which:
In this problem:
Then, the equation is:
[tex]y = A\sin{(2\pi fx)}[/tex]
[tex]y = 1.5\sin{(2\pi (262)x)}[/tex]
[tex]y = 1.5\sin{(524\pi x)}[/tex]
A similar problem, which also involves building a sine function according to the desired characteristics, is given at https://brainly.com/question/18055768
