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Interference between the transverse and longitudinal vibrations in musical strings
Institution:Moscow, Russia;Institute of Applied Mathematics and Mechanics of the National Academy of Sciences of Ukraine, Donetsk, Ukraine;Moscow, Russia;Dorodnicyn Computing Centre of the Russian Academy of Sciences, Moscow, Russia;Institute for Precision Mechanics and Control Problems Russ. Acad. of Sci., Saratov, Russia;Moscow, Russia;Moscow Institute of Physics and Technology, Dolgoprudnyi, Russia
Abstract:Two problems of the vibrations of strings are considered using the approach described previously in 1]: the vibrations of the string of a plucked musical instrument, drawn out at one of the points and at rest at the initial instant of time (Problem 1), and the vibrations of the string of a keyboard musical instrument, the points of which are given an initial velocity at the initial instant of time by a hammer of small width (Problem 2). It is established that forced longitudinal oscillations of the string occur at frequencies of the transverse vibrations, the condition for possible resonance of the longitudinal vibrations is derived, and the nature of the vibrations at the point where the string is fastened due to elasticity and the related shift in the frequency of transverse vibrations is established.
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