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Chapter 7: Q7P (page 347)

Use a trigonometry formula to write the two terms as a single harmonic. Find the period and amplitude. Compare computer plots of your result and the given problem.

cosπx-cosπ(x-1/2)

Short Answer

Expert verified

The period and amplitude are T = 2 and A=2.

Step by step solution

01

Given information

A fundamental musical tone and some of its overtones of harmonics are:

cosπx-cosπ(x-1/2)

02

Formula of trigonometry

Trigonometry formula is[sina+sinb=2sina+b2cosa-b2].

03

Write the two terms as a single harmonic

The given harmonic term iscosπx-cosπ(x-1/2).

=-2sinπx+πx-π/22sinπx+πx-π/22=-2sinπx-π4sinπ4=-2sinπx-14

Thus,the period and amplitude are T = 2 and A=2.

04

The computer plots of the start and end functions

The plot of start of the function is shown below

And, plot of function is shown below.end of the

Thus, the period and amplitude are T = 2 and A=2.

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