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

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edited 9 mins ago

knzhou

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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

share|cite|improve this question

edited 9 mins ago

knzhou

33.9k897170

asked 3 hours ago

Artificial Stupidity

1265

add a comment | 

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

share|cite|improve this question

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

share|cite|improve this question

edited 9 mins ago

knzhou

33.9k897170

asked 3 hours ago

Artificial Stupidity

1265

share|cite|improve this question

edited 9 mins ago

knzhou

33.9k897170

asked 3 hours ago

Artificial Stupidity

1265

share|cite|improve this question

share|cite|improve this question

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 | 

add a comment | 

3 Answers
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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.

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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.

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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.

share|cite|improve this answer

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.

• 
  
  
  

  
  

  
  
  
  
  
  

  
  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 | 

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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.

share|cite|improve this answer

answered 3 hours ago

S. McGrew

4,0132621

add a comment | 

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.

share|cite|improve this answer

answered 3 hours ago

S. McGrew

4,0132621

add a comment | 

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.

share|cite|improve this answer

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.

share|cite|improve this answer

answered 3 hours ago

S. McGrew

4,0132621

share|cite|improve this answer

share|cite|improve this answer

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 | 

add a comment | 

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.

share|cite|improve this answer

answered 3 hours ago

Maxim Umansky

2,83831025

add a comment | 

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.

share|cite|improve this answer

answered 3 hours ago

Maxim Umansky

2,83831025

add a comment | 

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.

share|cite|improve this answer

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.

share|cite|improve this answer

answered 3 hours ago

Maxim Umansky

2,83831025

share|cite|improve this answer

share|cite|improve this answer

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 | 

add a comment | 

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.

share|cite|improve this answer

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.

• 
  
  
  

  
  

  
  
  
  
  
  

  
  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 | 

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.

share|cite|improve this answer

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.

• 
  
  
  

  
  

  
  
  
  
  
  

  
  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 | 

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.

share|cite|improve this answer

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.

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.

share|cite|improve this answer

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.

share|cite|improve this answer

share|cite|improve this answer

edited 1 hour ago

edited 1 hour ago

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 | 

• 
  
  
  

  
  

  
  
  
  
  
  

  
  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 | 

 

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