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Explanation of Sound or Music from a String by Ron Kurtus - Succeed in Understanding Physics. Also refer to physical science, harmonics, wire, vibration, tension, length, mass, wavelength, School for Champions. Copyright © Restrictions
Sound or Music from a String
by Ron Kurtus (8 January 2008)
When you attach a string or wire between two posts and pull it tight, you can create sound or musical notes by plucking on the string. The vibration of the string will create a fundamental frequency, according to the dimensions of the string. The string can also vibrate at multiples of its fundamental frequency. These are called harmonics. You can hear such effects in stringed instruments such as a guitar and violin.
Questions you may have include:
- How does a plucked string create vibrations?
- How does a vibrating string create sound?
- What are the harmonics in the string?
This lesson will answer those questions. There is a mini-quiz near the end of the lesson.
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Plucked string 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.
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 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.
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.
String vibrating at 2nd harmonic
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.
See the Side Menu for more topics on Sound Waves
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Resources and references
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Mini-quiz to check your understanding
If you got all three correct, you are on your way to becoming a Champion in Physics. If you had problems, you had better look over the material again.
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Sound or Music from a String