Chapter 6.7B, Problem 7GCE

To determine

To write two sine functions with almost equal frequencies and graph the sum of two functions and discuss any two interesting features of graph.

Explanation of Solution

The following are the two functions having the almost same frequency −

Function 1- $f(x)=\sin (4\pi x)$

Function 2- $f(x)=\sin (3.89\pi x)$

The sum of the above two functions will be

  $f(x)=\sin (4\pi x)+\sin (3.89\pi x)$ And window is $\left[0,10\pi \right]\text{ scl:}\pi$ by $\left[-2.5,2.5\right]\text{ scl:1}$

The following is the graph of the sum function-

  

The following is the interesting feature- The aspect is here window size, if the window size is less, the value of function couldn’t be found for the given value of $x$ but if the window size is increased, the solution is visible in the graphing calculator.