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A violin string of length L=31.8 cm and linear mass density µ=0.64gm/is tuned to play an A4 note at 440.0 Hz. This means that the string is in its mode of oscillation fundamental, that is, it will be on that note without placing any fingers on it. From this information, A. Calculate the tension in the string that will keep it in tune. B. If the midpoint of the string is observed to have a maximum transverse motion of 2.59 mm when in the fundamental mode, what is the maximum speed vy máx of the antinode of the string? c. If the string tension is reduced by 6.3% of the tension found in part A, what is the resulting frequency of the note produced? D. When playing the violin, different notes can be produced depending on the position of the fingers of one hand on the string. The usual technique presses the string hard against the fretboard, reducing the length of the string that can vibrate. If we consider this string initially tuned for an A4, and a finger is placed a third of the way down from the headstock: What would be the new fundamental frequency, that is, the frequency of the new note that is being produced assuming it has the same tension as in part A? What would be the new frequency of the note, if instead of using the technique i. ii. described above for violin playing, the technique called artificial harmonic is used, where the string is only partially pressed in such a way as to produce a node on the string?

A violin string of length L=31.8 cm and linear mass density µ=0.64gm/is tuned to play an A4 note at 440.0 Hz. This means that the string is in its mode of oscillation fundamental, that is, it will be on that note without placing any fingers on it. From this information, A. Calculate the tension in the string that will keep it in tune. B. If the midpoint of the string is observed to have a maximum transverse motion of 2.59 mm when in the fundamental mode, what is the maximum speed vy máx of the antinode of the string? c. If the string tension is reduced by 6.3% of the tension found in part A, what is the resulting frequency of the note produced? D. When playing the violin, different notes can be produced depending on the position of the fingers of one hand on the string. The usual technique presses the string hard against the fretboard, reducing the length of the string that can vibrate. If we consider this string initially tuned for an A4, and a finger is placed a third of the way down from the headstock: What would be the new fundamental frequency, that is, the frequency of the new note that is being produced assuming it has the same tension as in part A? What would be the new frequency of the note, if instead of using the technique i. ii. described above for violin playing, the technique called artificial harmonic is used, where the string is only partially pressed in such a way as to produce a node on the string?

Principles of Physics: A Calculus-Based Text
Principles of Physics: A Calculus-Based Text
5th Edition
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Raymond A. Serway, John W. Jewett
Chapter14: Superposition And Standing Waves
Section: Chapter Questions
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A violin string of length L=31.8 cm and linear mass density µ=0.64gm/is tuned to play an A4 note at 440.0 Hz. This means that the string is in its mode of oscillation fundamental, that is, it will be on that note without placing any fingers on it. From this information, A. Calculate the tension in the string that will keep it in tune. B. If the midpoint of the string is observed to have a maximum transverse motion of 2.59 mm when in the fundamental mode, what is the maximum speed vy máx of the antinode of the string? C. If the string tension is reduced by 6.3% of the tension found in part A, what is the resulting frequency of the note produced? D. When playing the violin, different notes can be produced depending on the position of the fingers of one hand on the string. The usual technique presses the string hard against the fretboard, reducing the length of the string that can vibrate. If we consider this string initially tuned for an A4, and a finger is placed a third of the way down from the headstock: What would be the new fundamental frequency, that is, the frequency of the new note that is being produced assuming it has the same tension as in part A? What would be the new frequency of the note, if instead of using the technique i. ii. described above for violin playing, the technique called artificial harmonic is used, where the string is only partially pressed in such a way as to produce a node on the string?
Transcribed Image Text:A violin string of length L=31.8 cm and linear mass density µ=0.64gm/is tuned to play an A4 note at 440.0 Hz. This means that the string is in its mode of oscillation fundamental, that is, it will be on that note without placing any fingers on it. From this information, A. Calculate the tension in the string that will keep it in tune. B. If the midpoint of the string is observed to have a maximum transverse motion of 2.59 mm when in the fundamental mode, what is the maximum speed vy máx of the antinode of the string? C. If the string tension is reduced by 6.3% of the tension found in part A, what is the resulting frequency of the note produced? D. When playing the violin, different notes can be produced depending on the position of the fingers of one hand on the string. The usual technique presses the string hard against the fretboard, reducing the length of the string that can vibrate. If we consider this string initially tuned for an A4, and a finger is placed a third of the way down from the headstock: What would be the new fundamental frequency, that is, the frequency of the new note that is being produced assuming it has the same tension as in part A? What would be the new frequency of the note, if instead of using the technique i. ii. described above for violin playing, the technique called artificial harmonic is used, where the string is only partially pressed in such a way as to produce a node on the string?
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