Chapter 8.5, Problem 57AYU

To determine

To find: The graph for the sound emitted by touching 7.

Answer to Problem 57AYU

The required graph is shown in Figure 1

Explanation of Solution

Given:

The given diagram is shown in Figure 1

  

Figure 1

The sound produced by the dial pad is the sum of two tones given by $y=\sin \left(2\pi lh\right)$ and $y=\sin \left(2\pi ht\right)$ .

The low frequency on touching 7 is $l=852\text{cycles}$ and the high frequency is $h=1209\text{cycles}$ .

The expression for the sound emitted by touching 7 is $y=\sin \left[2\pi \left(852\right)t\right]+\sin \left[2\pi \left(1209\right)t\right]$ .

Calculation:

Consider the sine function for the sound emitted by 7 is,

  $y=\sin \left[2\pi \left(852\right)t\right]+\sin \left[2\pi \left(1209\right)t\right]$

Then, from the high and the low sound frequency.

  $\begin{array}{c}y=\sin \left[2\pi \left(852\right)t\right]+\sin \left[2\pi \left(1209\right)t\right]\\ =\sin \left[1704\pi t\right]+\sin \left[2418\pi t\right]\end{array}$

By the use of maple the graph for the sound emitted by 7 is shown in Figure 1

  

Figure 1