5. Electric guitar strings are made of steel (density 8 g/cm') and are stretched along a fixed 65 cm length, where they can create standing waves when plucked. Although the standing wave does not move, it can be thought of as the sum of two traveling waves with equal speeds going in opposite directions: ym Ssin(kx - wt) + Ym sin(kx + wt). The lowest string on a guitar is typically 1.2 mm in diameter and is usually tuned to an "E" of 82 Hz, though the note it makes can be adjusted by changing the tension of the string. A) What is the wavelength of the fundamental tone made by this string? B) What speed should the traveling waves that make up the standing wave have in order for the string to produce an 82 Hz E as its fundamental tone? C) What tension should the string have in order produce an 82 Hz E? D) The fundamental tone corresponds to the n integer index of standing waves being equal to 1, while the overtones of this string correspond to n 2, 3, 4, 5.. What is the index value for the overtone of this string that matches the "B" string of the guitar, which has a fundamental frequency of 246 Hz? E) From 0 to 65 cm, at what points on the string are the nodes of this "B" overtone?
5. Electric guitar strings are made of steel (density 8 g/cm') and are stretched along a fixed 65 cm length, where they can create standing waves when plucked. Although the standing wave does not move, it can be thought of as the sum of two traveling waves with equal speeds going in opposite directions: ym Ssin(kx - wt) + Ym sin(kx + wt). The lowest string on a guitar is typically 1.2 mm in diameter and is usually tuned to an "E" of 82 Hz, though the note it makes can be adjusted by changing the tension of the string. A) What is the wavelength of the fundamental tone made by this string? B) What speed should the traveling waves that make up the standing wave have in order for the string to produce an 82 Hz E as its fundamental tone? C) What tension should the string have in order produce an 82 Hz E? D) The fundamental tone corresponds to the n integer index of standing waves being equal to 1, while the overtones of this string correspond to n 2, 3, 4, 5.. What is the index value for the overtone of this string that matches the "B" string of the guitar, which has a fundamental frequency of 246 Hz? E) From 0 to 65 cm, at what points on the string are the nodes of this "B" overtone?
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Transcribed Image Text:5. Electric guitar strings are made of steel (density 8 g/cm') and are stretched along a fixed 65 cm
length, where they can create standing waves when plucked. Although the standing wave does not
move, it can be thought of as the sum of two traveling waves with equal speeds going in opposite
directions: ym sin(kx - wt) + Ym sin(kx + wt). The lowest string on a guitar is typically 1.2 mm in
diameter and is usually tuned to an "E" of 82 Hz, though the note it makes can be adjusted by
changing the tension of the string.
A) What is the wavelength of the fundamental tone made by this string?
B) What speed should the traveling waves that make up the standing wave have in order for the
string to produce an 82 Hz E as its fundamental tone?
C) What tension should the string have in order produce an 82 Hz E?
D) The fundamental tone corresponds to the n integer index of standing waves being equal to 1,
while the overtones of this string correspond to n = 2, 3, 4, 5... What is the index value for the
overtone of this string that matches the "B" string of the guitar, which has a fundamental
frequency of 246 Hz?
E) From 0 to 65 cm, at what points on the string are the nodes of this "B" overtone?
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