Question

The displacement, d, in millimeters of a tuning fork as a function of time, t, in seconds can be modeled with the equation d = 0.6 sine (3520 pi t). What is the frequency of the tuning fork?

Answer 1

Answer:

The frequency of the tuning fork is 1760 Hz.

Step-by-step explanation:

Suppose we have a sine function in the following format:

$y = A\sin{Bx + C}$

The period is:

$T = \frac{2\pi}{B}{/tex]The frequency, in Hz, is:[tex]F = \frac{1}{T}$

In this question:

$d = 0.6\sin{3520\pi t}$

So

$B = 3520\pi, T = \frac{2\pi}{3520} = \frac{2}{3520}, F = \frac{1}{T} = \frac{1}{\frac{2}{3520}} = \frac{3520}{2} = 1760$

The frequency of the tuning fork is 1760 Hz.