Home Forums Blogs Articles Photos Videos Contact FAQ

Vibrating string

Vibrating string: Encyclopedia - Vibrating string

A vibration in a string is a wave. Usually a vibrating string produces a sound whose frequency is constant. Therefore, since frequency characterizes the pitch, the sound produced is a constant note. Vibrating strings are the basis of any string instrument like guitar, cello, or piano. Vibrating string - Speed of propagation of the wave. Let L be the length of the string, m its mass and T the tension.< ...

Including:

Vibrating string - Speed of propagation of the wave

Vibrating string - Frequency of the wave

Vibrating string - Miscellaneous

Vibrating string, Vibrating string - Frequency of the wave, Vibrating string - Miscellaneous, Vibrating string - Speed of propagation of the wave, String instruments, Fretted instruments, Physics of music, Pitch

Vibrating string: Encyclopedia - Vibrating string

Vibrating string

A vibration in a string is a wave. Usually a vibrating string produces a sound whose frequency is constant. Therefore, since frequency characterizes the pitch, the sound produced is a constant note. Vibrating strings are the basis of any string instrument like guitar, cello, or piano.

Vibrating string - Speed of propagation of the wave

Let L be the length of the string, m its mass and T the tension.

When the string is touched it bends as an arc of circle. Let R be the radius and θ the angle under the arc. Then .

The string is recalled to its natural position by a force F:

The force F is also equal to the centripetal force

where v is the speed of propagation of the wave in the string.

Let μ be the linear mass of the string. Then

and

If we equate the two expressions for F, we have:

Solving for velocity v, we find

String instruments, Fretted instruments, Physics of music, Pitch

Vibrating string - Frequency of the wave

Once we know the speed of propagation, it is almost immediate to find the frequency of the sound produced by the string. In fact we know that the speed of propagation of a wave is equal to the wavelength λ divided by the period T, or multiplied by the frequency f :

If the length of the string is L, the fundamental harmonic is the one produced by the vibration whose nodes are the two ends of the string, so L is half of the wavelength of the fundamental harmonic.

Hence:

where T is the tension, μ is the linear mass, and L is the length of the vibrating part of the string. Therefore:

the shorter the string, the higher the note
the higher the tension, the higher the note
the heavier the string, the lower the note

Vibrating string - Miscellaneous

It is interesting that one can actually see the waveforms on a vibrating string if the frequency is low enough and the vibrating string is held in front of a computer monitor.