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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.
Mersenne's laws govern the construction and operation of string instruments, such as pianos and harps, which must accommodate the total tension force required to keep the strings at the proper pitch. Lower strings are thicker, thus having a greater mass per length. They typically have lower tension. Guitars are a familiar exception to this ...
Vibration, standing waves in a string. The fundamental and the first 5 overtones in the harmonic series. 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.
where is the applied tension on the line, is the resulting force exerted at the other side of the capstan, is the coefficient of friction between the rope and capstan materials, and is the total angle swept by all turns of the rope, measured in radians (i.e., with one full turn the angle =).
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. String theory is a broad and varied subject that attempts to address a number of deep questions of fundamental physics.
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 tuning fork , later ...
Figure 1: Two spheres tied with a string and rotating at an angular rate ω. Because of the rotation, the string tying the spheres together is under tension. Figure 2: Exploded view of rotating spheres in an inertial frame of reference showing the centripetal forces on the spheres provided by the tension in the tying string.
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 ...