Trigonometry (11th Edition) Clone

Published by Pearson
ISBN 10: 978-0-13-421743-7
ISBN 13: 978-0-13421-743-7

Chapter 6 - Inverse Circular Functions and Trigonometric Equations - Section 6.3 Trigonometric Equations II - 6.3 Exercises - Page 280: 57b

Answer

The graph is a close approximation of a square wave. The sound wave has a shape that is similar to a square wave with some slight fluctuations in amplitude in places where a square wave is normally flat. Also, a square wave has vertical lines connecting the positive values and negative values. Although the graph of this sound wave has lines connecting positive values and negative values which are not vertical, the slope of these connecting lines are steep and close to vertical. Again, the graph of this sound wave is a close approximation of a square wave.
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Work Step by Step

$P = 0.003~sin~220~\pi~t+\frac{0.003}{3}~sin~660~\pi~t+\frac{0.003}{5}~sin~1100~\pi~t+\frac{0.003}{7}~sin~1540~\pi~t$ We can see a sketch of the graph in the viewing window $[0,0.03]$ by $[-0.005, 0.005]$ The graph of this sound wave is a close approximation of a square wave. The sound wave has a shape that is similar to a square wave with some slight fluctuations in amplitude in places where a square wave is normally flat. Also, a square wave has vertical lines connecting the positive values and negative values. Although the graph of this sound wave has lines connecting positive values and negative values which are not vertical, the slope of these connecting lines are steep and close to vertical. Again, the graph of this sound wave is a close approximation of a square wave.
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