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(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 for the following. (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 di 20 and L is-Select--fis-Select----Select.. (ii) when the tension is increased by turning a tuning peg 20 and T is-Select-fis-Select--Select-- (iii) when the linear density is increased by switching to another string 70 and p is-Select-fis-Select--Select-- dp

(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 for the following. (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 di 20 and L is-Select--fis-Select----Select.. (ii) when the tension is increased by turning a tuning peg 20 and T is-Select-fis-Select--Select-- (iii) when the linear density is increased by switching to another string 70 and p is-Select-fis-Select--Select-- dp

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 94E
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Please answer part B

The frequency of vibrations of a vibrating violin string is given by = 2√ f= where L is the length of the string, T is its tension, and p is its linear density. (a) Find the rate of change of the frequency with respect to the following. (1) the length (when T and p are constant) (ii) the tension (when L and p are constant) (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 for the following. (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 20 and L is --Select--fis---Select-----Select-- (ii) when the tension is increased by turning a tuning peg 70 and Tis ---Select--fis --Select--→---Select-- Answer options: , >, <, increasing, decreasing, lower, higher. (iii) when the linear density is increased by switching to another string 20 and p is-Select--fis-Select--Select-- dp
Transcribed Image Text:The frequency of vibrations of a vibrating violin string is given by = 2√ f= where L is the length of the string, T is its tension, and p is its linear density. (a) Find the rate of change of the frequency with respect to the following. (1) the length (when T and p are constant) (ii) the tension (when L and p are constant) (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 for the following. (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 20 and L is --Select--fis---Select-----Select-- (ii) when the tension is increased by turning a tuning peg 70 and Tis ---Select--fis --Select--→---Select-- Answer options: , >, <, increasing, decreasing, lower, higher. (iii) when the linear density is increased by switching to another string 20 and p is-Select--fis-Select--Select-- dp
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