MyLab Math with Pearson eText -- 24-Month Standalone Access Card -- for Trigonometry

11th Edition

ISBN: 9780135909140

Author: Lial, Margaret, HORNSBY, John, SCHNEIDER, David, DANIELS, Callie

Publisher: PEARSON

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Textbook Question

Chapter 6.3, Problem 59E

Hearing Difference Tones When a musical instrument creates a tone of 110 Hz, it also creates tones at 220. 330. 440. 550. 660, … Hz. A small speaker cannot reproduce the 110-Hz vibration but it can reproduce the higher frequencies, which are the upper harmonics. The low tones can still be heard because the speaker produces difference tones of the upper harmonics. The difference between consecutive frequencies is 110 Hz. and this difference tone will be heard by a listener. (Source: Benade. A., Fundamentals of Musical Acoustics. Dover Publications.)

(a) In the window [0.0.03] by [-1,1], graph the upper harmonics represented by the pressure

P = 1 2 sin [ 2 π ( 220 ) t ] + 1 3 sin [ 2 π ( 330 ) t ] + 1 4 sin [ 2 π ( 440 ) t ] .

(b) Estimate all t-coordinates where P is maximum.

(c) What does a person hear in addition to the frequencies of 220. 330. and 440 Hz?

(d) Graph the pressure produced by a speaker that can vibrate at 110 Hz and above.

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Chapter 6.3, Problem 58E

Chapter 6.3, Problem 60E

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Chapter 6 Solutions

MyLab Math with Pearson eText -- 24-Month Standalone Access Card -- for Trigonometry

Ch. 6.1 - CONCEPT PREVIEW Fill in the blank(s) to...Ch. 6.1 - CONCEPT PREVIEW Fill in the blank(s) to...Ch. 6.1 - 3. y = cos–1 x means that x = ________ for 0 ≤ y...Ch. 6.1 - 4. The point lies on the graph of y = tan x....Ch. 6.1 - 5. If a function f has an inverse and f(π) = –1,...Ch. 6.1 - CONCEPT PREVIEW Fill in the blank(s) to...Ch. 6.1 - CONCEPT PREVIEW Write a short answer for each of...Ch. 6.1 - Consider the inverse cosine function y = cos1 x,...Ch. 6.1 - 9. Consider the inverse tangent function y =...Ch. 6.1 - 10. Give the domain and range of each inverse...

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Solution Summary: The author explains how to graph the upper harmonics represented by the pressure in the window.

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