Sound Waves Have you ever looked closely at sound waves? They may look like random lines at first glance. But if you zoom in, you will see that they are very similar to graphs of trigonometric functions. Like trigonometric functions, they appear as oscillating waves with a measurable frequency and amplitude. In music, each note has a specific frequency, measured in hertz. The units for hertz are cycles per second (1 + sec), or sec"]. The most common note used for tuning an instrument is the A next to middle C. Pianists often call this note A4. This note has a frequency of 440 Hz. This means that the note A4 has 440 cycles in one second. Any musical note can be graphed using the function f(x) = sin (y x 2nux), where y is the frequency of the note and x is the time in seconds. Part A Using this graphing tool @ , graph the function for note A4. Paste a copy of the graph below, keeping the default scale. What does it look like? Why does it appear like that? BIYXX , 15px AvLY Characters used: 0 / 15000Part B Now change the scale of the graph. Go back to the graphing tool and scroll down to adjust the minimum and maximum values of x and y. Change the minimum value of x to -0.01 and the maximum value to 0.01. Change the minimum value for y to -1.5 and the maximum value to 1.5. Graph the function again and paste a screenshot of it below. What does the graph look like now? What is the amplitude of the wave? What is the period of the wave? The period of a wave is the time it takes for one wavelength, or cycle, to pass a given point. It is the inverse of the wave's frequency. B IYXX , 15px BVB Characters used: 0 / 15000 Part C A musician usually plays more than one note at a time; these are called harmonies. If you play three or more notes at once, you get a chord. An example of a chord is A-C#-E. Each of these notes has a different frequency. The frequency of A is 440 Hz, the frequency of C# is 554.37 Hz, and the frequency of E is 659.25 Hz. Create a function for each note, and then add them to create a combination function for the chord A-C#-E. Write all four of these functions in your response. Graph the combination function, keeping the scale of the graph similar to the scale you used in part b. Paste a copy of the graph below. BIYXX , 15px w BVB Characters used: 0 / 15000Part D Compare the graphs from parts b and c. What are some similarities and differences between the two graphs? B IY XX , 15px BVB Characters used: 0 / 15000 Part E Noise-cancelling headphones target the undesirable sound waves that you would hear without the headphones. Then they emit a sound wave that is a reflection across the x-axis of the undesirable sound wave. To see this on a graph, consider the note A, again. The sound wave needed to cancel this note out is represented by the function f(x) = sin(880 * It (X - p )). Add this function to the function for A4 and graph the combination of these functions using the default dimensions. Paste the graph below. What does the graph look like? What does it indicate about the sound produced? B IYXX , 15px B . VB Characters used: 0/ 15000