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A vibration in a string is a wave. Resonance causes a vibrating string to produce a sound with constant frequency, i.e. constant pitch. If the length or tension of the string is correctly adjusted, the sound produced is a musical tone. Vibrating strings are the basis of string instruments such as guitars, cellos, and pianos.
Mersenne's laws. A string half the length (1/2), four times the tension (4), or one-quarter the mass per length (1/4) is an octave higher (2/1). If the tension on a string is ten lbs., it must be increased to 40 lbs. for a pitch an octave higher. [1] Mersenne's laws are laws describing the frequency of oscillation of a stretched string or ...
The wave equation is a hyperbolic partial differential equation describing waves, including traveling and standing waves; the latter can be considered as linear superpositions of waves traveling in opposite directions. This article mostly focuses on the scalar wave equation describing waves in scalars by scalar functions u = u (x, y, z, t) of a ...
Melde's experiment. A model of Melde's experiment: an electric vibrator connected to a cable drives a pulley that suspends a mass that causes tension in the cable. Melde's experiment is a scientific experiment carried out in 1859 by the German physicist Franz Melde on the standing waves produced in a tense cable originally set oscillating by a ...
Sympathetic resonance. Sympathetic resonance or sympathetic vibration is a harmonic phenomenon wherein a passive string or vibratory body responds to external vibrations to which it has a harmonic likeness. [1] The classic example is demonstrated with two similarly-tuned tuning forks. When one fork is struck and held near the other, vibrations ...
A vibrating string vibrates with a set of frequencies that depend on the string's tension. These frequencies can be derived from Newton's laws of motion. Each microscopic segment of the string pulls on and is pulled upon by its neighboring segments, with a force equal to the tension at that position along the string. If the string has curvature ...
For an ideal string, the dispersion relation can be written as =, where T is the tension force in the string, and μ is the string's mass per unit length. As for the case of electromagnetic waves in vacuum, ideal strings are thus a non-dispersive medium, i.e. the phase and group velocities are equal and independent (to first order) of vibration ...
Vibration and standing waves in a string, The fundamental and the first six overtones. The fundamental frequency, often referred to simply as the fundamental (abbreviated as f 0), is defined as the lowest frequency of a periodic waveform. [1] In music, the fundamental is the musical pitch of a note that is perceived as the lowest partial present.