Q36. - Algebra 2

Question

If the amplitude of the sine function is $0.25$, write the equations for tuning forks that resonate with a frequency of $64,256$, and $512$ Hertz.

Step-by-Step Solution

Answer

The equations of tuning fork with frequencies $64,256$ and $512$ hertz, are $y=0.25\sin 128\pi t$, $y=0.25\sin 512\pi t$ and $y=0.25\sin 1024\pi t$ respectively.  

Step 1. Given information

A tuning fork with amplitude 0.25 and three different frequencies is given.

Step 2. Concept used

Put the values of amplitude and frequencies in the general equation and simplify it.

The general equation is-

$y=A\sin \omega t$

Where $A=$ amplitude and $\omega =$ angular frequency

Step 3. Calculation

First we have to find the value of angular frequency as-

$\omega =2\pi f$

For $f=64$,

 $\begin{array}{l}y=A\sin \omega t\\ y=0.25\sin (2\pi \times 64)t\\ y=0.25\sin 128\mathrm{\pi }t\end{array}$

For $f=256$,

 $\begin{array}{l}y=A\sin \omega t\\ y=0.25\sin (2\pi \times 256)t\\ y=0.25\sin 512\mathrm{\pi }t\end{array}$

For $f=512$,

$\begin{array}{l}y=A\sin \omega t\\ y=0.25\sin (2\pi \times 512)t\\ y=0.25\sin 1024\mathrm{\pi }t\end{array}$