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When plucked, the high E string on a guitar has a frequency of 330 cycles per second. What sine function represents this note when it is graphed with an amplitude of 1.5 units? Let x represent the number of seconds. Enter your exact answer in the box.

Respuesta :

Let's analyse the function

[tex]y = f(x) = A\sin(\omega x)[/tex]

The amplitude is A, so we want A=1.5

Now, we start at x=0, and we have [tex]1.5\sin(0)=0[/tex]

After one second, i.e. x=1, we want this sine function to make 330 cycles, i.e. the argument must be [tex]330\cdot 2\pi[/tex]

So, we have

[tex]f(1)=1.5\sin(\omega) = 1.5\sin(660\pi)[/tex]

so, the function is

[tex]f(x) = 1.5\sin(660\pi x)[/tex]

Answer:

f(x) = 1.5\sin(660\pi x)

Step-by-step explanation:

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