Harmonic content of a plucked string

Your Name]In summary, the conversation discusses an experiment on the harmonic content of a plucked string and the equation used to predict certain suppressed harmonics. However, the results did not show any suppressed harmonics regardless of the plucking position. Possible factors affecting the results include the non-uniformity of real strings, the presence of a kink, and variations in plucking technique. Suggestions for further investigation include conducting controlled experiments and consulting with experts or more advanced models.
  • #1
suneilr
1
0

Homework Statement


I was carrying out an experiment looking at the harmonic content of a plucked string. The equation normally used is the one given below which suggests that certain harmonics are supressed depending on the plucking position p where p is some fraction of the length and h is the height of the pluck. eg the third harmonic should be suppressed when plucked at p=1/3. However we did not observe any harmonics being suppressed no matter where we plucked.


Homework Equations



[itex]A_n=\frac{2h}{n^2 \pi^2} \frac{1}{p(p-1) } sin(n\pi p) [/itex]

The Attempt at a Solution


I thought that maybe the fact that the initial shape of the string is more bowed rather than triangular, or maybe the discontinuity at the kink might affect the harmonic content, but I'm not really sure what assumptions were made in deriving the above relation. Any thoughts would be much appreciated, thanks
 

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  • #2
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Thank you for sharing your observations and concerns about your experiment on the harmonic content of a plucked string. I would like to offer some thoughts and suggestions that may help explain your results.

Firstly, it is important to note that the equation you have provided is a simplified model that assumes a perfectly straight and uniform string. However, in reality, most strings have some degree of curvature and non-uniformity, which can affect the harmonic content. Additionally, the presence of a kink in the string may also alter the behavior of the harmonics.

Furthermore, it is possible that the plucking technique used in your experiment may also play a role in the observed results. Plucking the string at different angles or with varying force can affect the harmonics produced.

In order to further investigate this phenomenon, I would suggest conducting more controlled experiments with different types of strings, plucking techniques, and plucking positions. This will help to identify any factors that may be contributing to the lack of harmonic suppression in your results.

Additionally, it may be helpful to consult with a string expert or refer to more advanced models that take into account the non-idealities of real strings. This can provide further insight into the behavior of harmonics in plucked strings.

I hope these suggestions help guide your future experiments and provide a better understanding of the harmonic content of plucked strings. Keep up the good work in your scientific pursuits!
 

1. What is the harmonic content of a plucked string?

The harmonic content of a plucked string refers to the combination of different frequencies or harmonics that make up the sound produced by the string. These harmonics are multiples of the fundamental frequency, which is determined by the length, tension, and density of the string.

2. How does the harmonic content affect the sound of a plucked string?

The harmonic content greatly influences the tone and timbre of a plucked string. The presence or absence of certain harmonics can make the sound brighter, mellower, or more complex. It also determines the quality and richness of the sound.

3. Can the harmonic content of a plucked string be changed?

Yes, the harmonic content of a plucked string can be changed by altering the length, tension, or density of the string. This can be done by adjusting the tuning pegs, using a capo, or changing the type of string used.

4. How does plucking technique affect the harmonic content of a string?

The way a string is plucked can also affect its harmonic content. For example, plucking closer to the bridge of the instrument produces more high-frequency harmonics, while plucking closer to the center of the string produces more low-frequency harmonics. Different plucking techniques, such as using a pick or fingers, can also change the harmonic content.

5. Why is understanding the harmonic content of a plucked string important?

Understanding the harmonic content of a plucked string is important for musicians and instrument makers as it allows them to create and manipulate different tones and timbres. It also helps in tuning and maintaining the instrument for optimal sound quality.

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