Question

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.

Answer 1

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

Explanation:

Answer 2

Let's analyse the function

`y = f(x) = A\sin(\omega x)`

The amplitude is A, so we want A=1.5

Now, we start at x=0, and we have
`1.5\sin(0)=0`

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

So, we have

`f(1)=1.5\sin(\omega) = 1.5\sin(660\pi)`

so, the function is

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