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-1. 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 × 2πx), 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?