When a tuning fork for middle C is struck, the resulting sound wave has a frequency of 262 cycles per second. The equation y = sin (262 · 2πx) is one possible model for this wave.
a. Identify the period of this wave. Make a graph showing about five complete cycles.
b. Suppose middle C on an out-of-tune piano is played and that the resulting wave has a frequency of 265 cycles per second. Write an equation to model the out-of-tune wave. Identify its period. Then make a graph using the same window as in 16a.
c. A piano tuner plays the out-of-tune C at the same time she uses the tuning fork. The two waves are added to produce a new sound wave. Write the equation that models the sum of the two waves. Graph a 0.5 s interval of this new equation.