Chapter 4.8, Problem 51E

To determine

To find: $\omega$ of the tuning fork where $\omega$ is a real number $>0$ .

Answer to Problem 51E

The $\omega$ of the tuning fork is $528\pi$ .

Explanation of Solution

Given information:

The simple harmonic motion of a point at the end of tuning fork is $d=a\sin \omega t$ and the frequency is also mentioned in the problem.

Formula used:

  $frequency$ $=\frac{\omega }{2\pi }$ $\Rightarrow \omega =2\pi *frequency$ .

Calculation:

Consider the statement that the simple harmonic motion of a point at the end of tuning fork is $d=a\sin \omega t$ .

Recall that the frequency of tuning fork is $264$ vibrations per second and $\omega =2\pi *frequency$ .

Therefore $\omega =2\pi *264=528\pi$ .

So, the $\omega$ of the tuning fork is $528\pi$ .