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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.
From this the mass per unit length of the string / wire can be derived. This is called as the principle of the Melde's Experiment Finding the mass per unit length of a piece of string is also possible by using a simpler method – a ruler and some scales – and this will be used to check the results and offer a comparison.
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] A string, tied at A, is kept in tension by W, a suspended weight, and two bridges, B and the movable bridge C ...
The wave equation in one space dimension can be derived in a variety of different physical settings. Most famously, it can be derived for the case of a string vibrating in a two-dimensional plane, with each of its elements being pulled in opposite directions by the force of tension. [2]
In string theory, one of the many vibrational states of the string corresponds to the graviton, a quantum mechanical particle that carries the gravitational force. Thus, string theory is a theory of quantum gravity .
Marin Mersenne, OM (also known as Marinus Mersennus or le Père Mersenne; French: [maʁɛ̃ mɛʁsɛn]; 8 September 1588 – 1 September 1648) was a French polymath whose works touched a wide variety of fields. He is perhaps best known today among mathematicians for Mersenne prime numbers, those written in the form M n = 2 n − 1 for some ...
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 or f 1), 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 ...