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Sound Created from a String or Wire

by Ron Kurtus (revised 12 March 2012)

By plucking on a string or wire that is pulled taut between two posts, you can create sounds or musical notes. The vibration creates a fundamental frequency, according to the dimensions of the string or wire, as well as its material.

The vibration can also be in multiples of the fundamental frequency. These are called harmonics. You can hear such effects in stringed instruments such as a guitar and violin.

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Plucked string or wire vibrates

When a string or wire is stretched tightly between two posts and then plucked, it will vibrate according to the length of the string. When the whole string vibrates as one, it is at its fundamental frequency.

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Fundamental frequency of a plucked string

Although the string or wire is taut, the material still will stretch somewhat when you pull on it or pluck it. You are applying a force on the string, and its elasticity and internal molecular forces cause it to bounce back to its original shape and beyond, thus resulting in the vibration.

The distance between the posts or the length of the string is half the wavelength of the string vibration, or L = ½λ, where λ is the Greek letter lambda, indicating wavelength. Note that this is not the wavelength of the sound created by the vibration. The sound wavelength is a function of the frequency of the string vibration.

(See Equation for Sound Created from a String for more information on that subject.)

Vibrating string creates sound

The string will vibrate at a frequency that is a function of the length, mass and tension of the string. That vibration causes the air to vibrate at the same frequency, making a sound or musical note.

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Vibrating string creates sound

If the parameters of the string or wire—the length, tension and mass—are correct, the sound made from plucking the string will be a musical note that is pleasing to the ear. But if they are slightly different, the sound may not be musical and just be a sound.

Harmonics in string

In most cases, the string will vibrate at the fundamental frequency or 1st harmonic. But if you pull the string harder, it can be made to vibrate with a shorter wavelength and higher frequency or the 2nd harmonic, 3rd harmonic or even higher.

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String vibrating at 2nd harmonic

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String vibrating at 3rd harmonic

If f1 is the frequency of the fundamental or 1st harmonic, then f2 = 2f1 is the frequency of the 2nd harmonic and f3 = 3f1is the frequency of the 3rd harmonic. This means that the sound from the higher harmonics is a higher pitch.

The wires used in a guitar or violin string are complex and never vibrate only in the 1st harmonic. In fact, they usually vibrate in a number of harmonics at once. This gives more quality to the sound.

Summary

By tightly attaching a string or wire between two posts and plucking on the string, you can create sound or musical notes. The vibration of the string will create a fundamental frequency, according to the dimensions of the string. The sound from this vibration is also at that frequency. The string can also vibrate at multiples or harmonics of its fundamental frequency. You can hear such effects in stringed instruments such as a guitar and violin.


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