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# The frequency of vibrations of a vibrating violin string is given by f 1 2L T where L is ISBN: 9781305270336 484

## Solution for problem 30 Chapter 3.7

Single Variable Calculus: Early Transcendentals | 8th Edition

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Problem 30

The frequency of vibrations of a vibrating violin string is given by f 1 2L T where L is the length of the string, T is its tension, and is its linear density. [See Chapter 11 in D. E. Hall, Musical Acoustics, 3rd ed. (Pacific Grove, CA: Brooks/Cole, 2002).] (a) Find the rate of change of the frequency with respect to (i) the length (when T and are constant), (ii) the tension (when L and are constant), and (iii) the linear density (when L and T are constant). (b) The pitch of a note (how high or low the note sounds) is determined by the frequency f. (The higher the frequency, the higher the pitch.) Use the signs of the derivatives in part (a) to determine what happens to the pitch of a note (i) when the effective length of a string is decreased by placing a finger on the string so a shorter portion of the string vibrates, (ii) when the tension is increased by turning a tuning peg, (iii) when the linear density is increased by switching to another string.

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##### ISBN: 9781305270336

Single Variable Calculus: Early Transcendentals was written by and is associated to the ISBN: 9781305270336. Since the solution to 30 from 3.7 chapter was answered, more than 225 students have viewed the full step-by-step answer. The answer to “The frequency of vibrations of a vibrating violin string is given by f 1 2L T where L is the length of the string, T is its tension, and is its linear density. [See Chapter 11 in D. E. Hall, Musical Acoustics, 3rd ed. (Pacific Grove, CA: Brooks/Cole, 2002).] (a) Find the rate of change of the frequency with respect to (i) the length (when T and are constant), (ii) the tension (when L and are constant), and (iii) the linear density (when L and T are constant). (b) The pitch of a note (how high or low the note sounds) is determined by the frequency f. (The higher the frequency, the higher the pitch.) Use the signs of the derivatives in part (a) to determine what happens to the pitch of a note (i) when the effective length of a string is decreased by placing a finger on the string so a shorter portion of the string vibrates, (ii) when the tension is increased by turning a tuning peg, (iii) when the linear density is increased by switching to another string.” is broken down into a number of easy to follow steps, and 182 words. This textbook survival guide was created for the textbook: Single Variable Calculus: Early Transcendentals, edition: 8. The full step-by-step solution to problem: 30 from chapter: 3.7 was answered by , our top Calculus solution expert on 03/19/18, 03:29PM. This full solution covers the following key subjects: . This expansive textbook survival guide covers 95 chapters, and 5427 solutions.

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