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How are overtones produced by plucking a string?
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I read the following from wikipedia:
When a string is plucked normally, the ear tends to hear the
fundamental frequency most prominently, but the overall sound is also
colored by the presence of various overtones (frequencies greater than
the fundamental frequency).
When I pluck a string, I just notice a node at each end and an antinode at the middle. How can we have overtones in addition to the fundamental frequency? It seems counterintuitive for me.
waves acoustics string harmonics
edited 9 mins ago
knzhou
33.9k897170
asked 3 hours ago
Artificial Stupidity
1265
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up vote
4
down vote
favorite
I read the following from wikipedia:
When a string is plucked normally, the ear tends to hear the
fundamental frequency most prominently, but the overall sound is also
colored by the presence of various overtones (frequencies greater than
the fundamental frequency).
When I pluck a string, I just notice a node at each end and an antinode at the middle. How can we have overtones in addition to the fundamental frequency? It seems counterintuitive for me.
waves acoustics string harmonics
edited 9 mins ago
knzhou
33.9k897170
asked 3 hours ago
Artificial Stupidity
1265
add a comment |Â
up vote
4
down vote
favorite
up vote
4
down vote
favorite
I read the following from wikipedia:
When a string is plucked normally, the ear tends to hear the
fundamental frequency most prominently, but the overall sound is also
colored by the presence of various overtones (frequencies greater than
the fundamental frequency).
When I pluck a string, I just notice a node at each end and an antinode at the middle. How can we have overtones in addition to the fundamental frequency? It seems counterintuitive for me.
waves acoustics string harmonics
edited 9 mins ago
knzhou
33.9k897170
asked 3 hours ago
Artificial Stupidity
1265
I read the following from wikipedia:
When a string is plucked normally, the ear tends to hear the
fundamental frequency most prominently, but the overall sound is also
colored by the presence of various overtones (frequencies greater than
the fundamental frequency).
When I pluck a string, I just notice a node at each end and an antinode at the middle. How can we have overtones in addition to the fundamental frequency? It seems counterintuitive for me.
waves acoustics string harmonics
waves acoustics string harmonics
edited 9 mins ago
knzhou
33.9k897170
asked 3 hours ago
Artificial Stupidity
1265
edited 9 mins ago
knzhou
33.9k897170
asked 3 hours ago
Artificial Stupidity
1265
edited 9 mins ago
knzhou
33.9k897170
edited 9 mins ago
knzhou
33.9k897170
edited 9 mins ago
knzhou
33.9k897170
33.9k897170
asked 3 hours ago
Artificial Stupidity
1265
asked 3 hours ago
Artificial Stupidity
1265
asked 3 hours ago
Artificial Stupidity
1265
1265
add a comment |Â
add a comment |Â
3 Answers
3
active
oldest
votes
up vote
12
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The only way to avoid overtones would be to pluck the string in such a way that its initial shape is sinusoidal. However, that would be nearly impossible. In practice, the initial shape is almost always triangular.
If you are familiar with Fourier transforms, consider how you would do a discrete Fourier decomposition of the string's initial shape. The Fourier components correspond to the overtones.
answered 3 hours ago
S. McGrew
4,0132621
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up vote
4
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Eigenmodes of a string have sinusoidal spatial form $f_m(x) = C_m sin(pi m x/L)$, where x is the parallel coordinate and L is the length of the string. Plucking a string at a fixed location $x_0 $means giving it a non-sinusoidal initial perturbation, e.g., something like a piece-wise linear function, $f(x) = A x/x_0$ for $x le x_0$ and $f(x) = A (L-x)/(L-x_0)$ for $x ge x_0$. Expanding the initial perturbation $f(x)$ in eigenmodes $f_m(x)$ shows how much each harmonic is excited initially, in general it would be a full spectrum of eigenmodes.
answered 3 hours ago
Maxim Umansky
2,83831025
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up vote
0
down vote
Although overtones exist, as a practical matter some may or may not be audible for human / hearing. (The same principle applies if transmitting the data, e.g. by telephone line). Some of the overtones would be at a frequency too high for humans to hear. Depending on your own hearing, you may not hear all of them.
answered 1 hour ago
JosephDoggie
1013
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JosephDoggie is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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I don't think this answers the question. If I understand it correctly, the question is why overtones (i.e. harmonics) exist for a plucked string. Your answer explains why some overtones may or may not be audible.
– Digital Trauma
1 hour ago
See edit. Certainly, the ability to hear tones is one of their properties (for example, consider the famous "If a tree falls in a forest and no one is there to hear it" question).
– JosephDoggie
1 hour ago
add a comment |Â
3 Answers
3
active
oldest
votes
3 Answers
3
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
12
down vote
The only way to avoid overtones would be to pluck the string in such a way that its initial shape is sinusoidal. However, that would be nearly impossible. In practice, the initial shape is almost always triangular.
If you are familiar with Fourier transforms, consider how you would do a discrete Fourier decomposition of the string's initial shape. The Fourier components correspond to the overtones.
answered 3 hours ago
S. McGrew
4,0132621
add a comment |Â
up vote
12
down vote
The only way to avoid overtones would be to pluck the string in such a way that its initial shape is sinusoidal. However, that would be nearly impossible. In practice, the initial shape is almost always triangular.
If you are familiar with Fourier transforms, consider how you would do a discrete Fourier decomposition of the string's initial shape. The Fourier components correspond to the overtones.
answered 3 hours ago
S. McGrew
4,0132621
add a comment |Â
up vote
12
down vote
up vote
12
down vote
The only way to avoid overtones would be to pluck the string in such a way that its initial shape is sinusoidal. However, that would be nearly impossible. In practice, the initial shape is almost always triangular.
If you are familiar with Fourier transforms, consider how you would do a discrete Fourier decomposition of the string's initial shape. The Fourier components correspond to the overtones.
answered 3 hours ago
S. McGrew
4,0132621
The only way to avoid overtones would be to pluck the string in such a way that its initial shape is sinusoidal. However, that would be nearly impossible. In practice, the initial shape is almost always triangular.
If you are familiar with Fourier transforms, consider how you would do a discrete Fourier decomposition of the string's initial shape. The Fourier components correspond to the overtones.
answered 3 hours ago
S. McGrew
4,0132621
answered 3 hours ago
S. McGrew
4,0132621
answered 3 hours ago
S. McGrew
4,0132621
answered 3 hours ago
S. McGrew
4,0132621
4,0132621
add a comment |Â
add a comment |Â
up vote
4
down vote
Eigenmodes of a string have sinusoidal spatial form $f_m(x) = C_m sin(pi m x/L)$, where x is the parallel coordinate and L is the length of the string. Plucking a string at a fixed location $x_0 $means giving it a non-sinusoidal initial perturbation, e.g., something like a piece-wise linear function, $f(x) = A x/x_0$ for $x le x_0$ and $f(x) = A (L-x)/(L-x_0)$ for $x ge x_0$. Expanding the initial perturbation $f(x)$ in eigenmodes $f_m(x)$ shows how much each harmonic is excited initially, in general it would be a full spectrum of eigenmodes.
answered 3 hours ago
Maxim Umansky
2,83831025
add a comment |Â
up vote
4
down vote
Eigenmodes of a string have sinusoidal spatial form $f_m(x) = C_m sin(pi m x/L)$, where x is the parallel coordinate and L is the length of the string. Plucking a string at a fixed location $x_0 $means giving it a non-sinusoidal initial perturbation, e.g., something like a piece-wise linear function, $f(x) = A x/x_0$ for $x le x_0$ and $f(x) = A (L-x)/(L-x_0)$ for $x ge x_0$. Expanding the initial perturbation $f(x)$ in eigenmodes $f_m(x)$ shows how much each harmonic is excited initially, in general it would be a full spectrum of eigenmodes.
answered 3 hours ago
Maxim Umansky
2,83831025
add a comment |Â
up vote
4
down vote
up vote
4
down vote
Eigenmodes of a string have sinusoidal spatial form $f_m(x) = C_m sin(pi m x/L)$, where x is the parallel coordinate and L is the length of the string. Plucking a string at a fixed location $x_0 $means giving it a non-sinusoidal initial perturbation, e.g., something like a piece-wise linear function, $f(x) = A x/x_0$ for $x le x_0$ and $f(x) = A (L-x)/(L-x_0)$ for $x ge x_0$. Expanding the initial perturbation $f(x)$ in eigenmodes $f_m(x)$ shows how much each harmonic is excited initially, in general it would be a full spectrum of eigenmodes.
answered 3 hours ago
Maxim Umansky
2,83831025
Eigenmodes of a string have sinusoidal spatial form $f_m(x) = C_m sin(pi m x/L)$, where x is the parallel coordinate and L is the length of the string. Plucking a string at a fixed location $x_0 $means giving it a non-sinusoidal initial perturbation, e.g., something like a piece-wise linear function, $f(x) = A x/x_0$ for $x le x_0$ and $f(x) = A (L-x)/(L-x_0)$ for $x ge x_0$. Expanding the initial perturbation $f(x)$ in eigenmodes $f_m(x)$ shows how much each harmonic is excited initially, in general it would be a full spectrum of eigenmodes.
answered 3 hours ago
Maxim Umansky
2,83831025
answered 3 hours ago
Maxim Umansky
2,83831025
answered 3 hours ago
Maxim Umansky
2,83831025
answered 3 hours ago
Maxim Umansky
2,83831025
2,83831025
add a comment |Â
add a comment |Â
up vote
0
down vote
Although overtones exist, as a practical matter some may or may not be audible for human / hearing. (The same principle applies if transmitting the data, e.g. by telephone line). Some of the overtones would be at a frequency too high for humans to hear. Depending on your own hearing, you may not hear all of them.
answered 1 hour ago
JosephDoggie
1013
New contributor
JosephDoggie is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
I don't think this answers the question. If I understand it correctly, the question is why overtones (i.e. harmonics) exist for a plucked string. Your answer explains why some overtones may or may not be audible.
– Digital Trauma
1 hour ago
See edit. Certainly, the ability to hear tones is one of their properties (for example, consider the famous "If a tree falls in a forest and no one is there to hear it" question).
– JosephDoggie
1 hour ago
add a comment |Â
up vote
0
down vote
Although overtones exist, as a practical matter some may or may not be audible for human / hearing. (The same principle applies if transmitting the data, e.g. by telephone line). Some of the overtones would be at a frequency too high for humans to hear. Depending on your own hearing, you may not hear all of them.
answered 1 hour ago
JosephDoggie
1013
New contributor
JosephDoggie is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
I don't think this answers the question. If I understand it correctly, the question is why overtones (i.e. harmonics) exist for a plucked string. Your answer explains why some overtones may or may not be audible.
– Digital Trauma
1 hour ago
See edit. Certainly, the ability to hear tones is one of their properties (for example, consider the famous "If a tree falls in a forest and no one is there to hear it" question).
– JosephDoggie
1 hour ago
add a comment |Â
up vote
0
down vote
up vote
0
down vote
Although overtones exist, as a practical matter some may or may not be audible for human / hearing. (The same principle applies if transmitting the data, e.g. by telephone line). Some of the overtones would be at a frequency too high for humans to hear. Depending on your own hearing, you may not hear all of them.
answered 1 hour ago
JosephDoggie
1013
New contributor
JosephDoggie is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Although overtones exist, as a practical matter some may or may not be audible for human / hearing. (The same principle applies if transmitting the data, e.g. by telephone line). Some of the overtones would be at a frequency too high for humans to hear. Depending on your own hearing, you may not hear all of them.
answered 1 hour ago
JosephDoggie
1013
New contributor
JosephDoggie is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited 1 hour ago
answered 1 hour ago
JosephDoggie
1013
New contributor
JosephDoggie is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
answered 1 hour ago
JosephDoggie
1013
answered 1 hour ago
JosephDoggie
1013
1013
New contributor
JosephDoggie is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
JosephDoggie is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
JosephDoggie is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
I don't think this answers the question. If I understand it correctly, the question is why overtones (i.e. harmonics) exist for a plucked string. Your answer explains why some overtones may or may not be audible.
– Digital Trauma
1 hour ago
See edit. Certainly, the ability to hear tones is one of their properties (for example, consider the famous "If a tree falls in a forest and no one is there to hear it" question).
– JosephDoggie
1 hour ago
add a comment |Â
I don't think this answers the question. If I understand it correctly, the question is why overtones (i.e. harmonics) exist for a plucked string. Your answer explains why some overtones may or may not be audible.
– Digital Trauma
1 hour ago
See edit. Certainly, the ability to hear tones is one of their properties (for example, consider the famous "If a tree falls in a forest and no one is there to hear it" question).
– JosephDoggie
1 hour ago
I don't think this answers the question. If I understand it correctly, the question is why overtones (i.e. harmonics) exist for a plucked string. Your answer explains why some overtones may or may not be audible.
– Digital Trauma
1 hour ago
I don't think this answers the question. If I understand it correctly, the question is why overtones (i.e. harmonics) exist for a plucked string. Your answer explains why some overtones may or may not be audible.
– Digital Trauma
1 hour ago
See edit. Certainly, the ability to hear tones is one of their properties (for example, consider the famous "If a tree falls in a forest and no one is there to hear it" question).
– JosephDoggie
1 hour ago
See edit. Certainly, the ability to hear tones is one of their properties (for example, consider the famous "If a tree falls in a forest and no one is there to hear it" question).
– JosephDoggie
1 hour ago
add a comment |Â
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