(a) Explanation Section 1: To determine: The linear mass density of the of the string E2 . Answer: The linear mass density of the string E2 is 0.0685 g/cm . Explanation: Given Info: The standard value of scale length of the guitar is 25.5 in , the typical tension of guitar string is 78.0 N and the wavelength of the fundamental wave is 129.54 cm . The following table shows the frequency of the corresponding strings. String E2 A2 D3 G3 B3 E4 f ( HZ ) 82.4 110.0 146.8 196.0 246.9 329.6 Formula to calculate the wavelength of the fundamental wave is, λ 1 = 2 L λ 1 is the wavelength of the fundamental wave. L is the length of the string. Substitute 25.5 in for L in the above equation to find λ 1 . λ 1 = 2 ( 25.5 in × 2.54 cm 1 in ) = 129.54 cm Thus, the wavelength of the fundamental wave is 129.54 cm . Formula to calculate the linear mass density of the string is, μ E2 = F v 2 (I) μ E2 is the linear mass density of the string. F is the tension on the string. v is the speed. Formula to calculate the speed of the wave is, v = λ 1 f E2 λ 1 is the fundamental wavelength. f E2 is the frequency of the wave. Substitute 129.54 cm for λ 1 and 82.4 Hz for f E2 in the above equation to find v . v = ( 129.54 cm ) ( 82.4 Hz ) = 106.741 m/s Thus, the speed of the wave is 106.741 m/s . Conclusion: Substitute 106.741 m/s for v and 78.0 N for F in the equation (I) to find μ E2 . μ E2 = 78.0 N ( 106.741 m/s ) 2 = ( 0.00685 kg/m ) ( 1000 g 1 kg ) ( 1 m 100 cm ) = 0.0685 g/cm Therefore, the linear mass density of the string E2 is 0.0685 g/cm . Section 2: To determine: The linear mass density of the of the string G3 . Answer: The linear mass density of the string G3 is 0.0121 g/cm . Explanation: Given Info: The standard value of scale length of the guitar is 25.5 in , the typical tension of guitar string is 78.0 N and the wavelength of the fundamental wave is 129.54 cm . Formula to calculate the linear mass density of the string is, μ G3 = F v 2 (II) μ G3 is the linear mass density of the string (b) To determine The tension in the replacement string to bring the fundamental frequency of the string E2 to the G3 value of 196.0 Hz .

14th Edition

ISBN: 9780133969290

Author: Hugh D. Young, Roger A. Freedman

Publisher: PEARSON

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Chapter 15, Problem 15.74P

(a)

To determine

The linear mass density of the of the string E2 , G3 and E4 .

(b)

To determine

The tension in the replacement string to bring the fundamental frequency of the string E2 to the G3 value of 196.0 Hz .

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Chapter 15, Problem 15.73P

Chapter 15, Problem 15.75P

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The linear mass density of the of the string E2 , G3 and E4 .

Solution Summary: The following table shows the frequency of the corresponding strings.

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The linear mass density of the of the string E2 , G3 and E4 .

The tension in the replacement string to bring the fundamental frequency of the string E2 to the G3 value of 196.0 Hz .

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Chapter 15 Solutions