Finding normal modes of a loaded string with the method of Lagrange multipliers

We consider the normal mode problem of a vibrating string loaded with n identical beads of equal spacing, which involves an eigenvalue problem. Unlike the conventional approach to solving this problem by considering the difference equation for the components of the eigenvector, we modify the eigenvalue equation by introducing matrix-valued Lagrange undetermined multipliers, which regularize the secular equation and make the eigenvalue equation non-singular. Then, the eigenvector can be obtained from the regularized eigenvalue equation by multiplying the indeterminate eigenvalue equation by the inverse matrix. We find that the inverse matrix is nothing but the adjugate matrix of the original matrix in the secular determinant up to the determinant of the regularized matrix in the limit that the constraint equation vanishes. The components of the adjugate matrix can be represented in simple factorized forms. Finally, one can directly read off the eigenvector from the adjugate matrix. We expect this new method to be applicable to other eigenvalue problems involving more general forms of the tridiagonal matrices that appear in classical mechanics or quantum physics.

Musical Bows in the Rock Art of Southern Africa

This is an advance summary of a forthcoming article in the Oxford Research Encyclopedia of Anthropology. Please check back later for the full article. The musical bow is speculated to have been discovered as a result of hunting, after a musical tone was heard from the vibrating string seconds after releasing the arrow. Some consider it the first musical instrument of the Bushman. A musical bow is an instrument that is made of a wooden stave that has a string attached to both ends of the stave, as well as, typically, a resonator. The musical bow belongs to the chordophone family, which comprises musical instruments that produce sound through the vibration of strings. Musical bows occur in southern African rock art specifically from South Africa and Namibia. In South Africa they are found in the Maloti Drakensberg massif, in the KwaZulu-Natal region, and in Maclear District in the Eastern Cape Province, whereas in Namibia they are found around the Daureb region. The occurrence of musical bows in the rock art of southern Africa hints at some of the musical instruments that were used during the Holocene period in the region. Their use as musical instruments is well documented ethnographically, and they are still used even today.

The effect of bamboo clip dimension and position towards the frequency spectrum of a vibrating inhomogeneous bundengan string

Bundengan is a traditional musical instrument from Indonesia. One of its unique features is the ability to produce sound imitating the gamelan, a percussive metallophone. This is generated by plucking on the bundengan strings, which have small bamboo clips attached to them. In this work, the effect of the clip dimension and position on the frequency spectrum of the vibrating string is analysed by means of computer simulation and experiment. The string was modelled using Scilab, taking into account the transversal and rotational vibration of the string and bamboo clip, including air drag force. The height to diameter ratio of the clip can be varied in the model. Furthermore, we set up a bundengan string on a sonometer with no resonator, attached specially made bamboo clips on it, and measured the sound frequency spectrum of the vibrating string. The results showed that increasing the height to diameter ratio of the clip decreased the overtone frequencies of the string. It was also found that the fundamental frequency of the string decreased, but its overtones increased, when the clip is shifted towards the middle of the string. The frequency spectrum from the simulation corresponds well to that from the experiment.

The Link between Electrical Properties of COVID-19 and Electromagnetic Radiation

The ability of a new vaccine design based on control the intracellular physiological consequences of both the electrical properties and the electromagnetic radiation interactions between a virus and a host cell, which is a method to strengthen immune system develop protection against COVID-19 and new strains. The capacity of COVID-19 to bind to angiotensin-converting enzyme 2 (ACE2) and immune evasion mechanisms are only one of the properties required to stimulate a preventative immune response. In this chapter, a multidimensional new strategy is used to exemplify the empowerment function intracellular and extracellular level information can play in the support of immunogen against COVID-19 pathogens. Besides during this chapter, the nature of electromagnetic radiation is described as a vibrating string based on a string-theory and unification of electromagnetic radiation and gravitational waves by supporting with multiple cites strong evidence. Overall, we demonstrate a new approach to understand the important role of the physiological consequences of the interplay between the immune system and COVID-19 and designing vaccine strategy immunogens that take advantage of that information against COVID-19 and new strains.

Model and Experiment on Resistance Loss of Wet Chordal Grid with Spray Pressure and Structural Parameters

To reduce the dedusting resistance of wet vibrating string grille precipitators during dedusting in mine ventilation roadways, we investigated the dedusting resistance characteristics of water fog and water film coupling and determined the relationship between dedusting resistance and spray pressure, vibrating grid filling rate, and wind speed. A mathematical resistance coefficient model is established using hydrodynamics theory and capillary mechanics. The theoretical relationship of dedusting resistance is deduced. The results show that when wind speed is constant, the spray pressure and dedusting resistance are higher and the resistance is smaller with a high filling rate compared with a low filling rate. Constant spray pressure allows faster wind speeds and reverse pressure gradient forces to increase when dust flows around the wet vibrating wire, which makes the pressure distribution asymmetrical around the steel wire and increases resistance. Dust removal resistance of the resonance chord with a high filling rate is substantially lower than that with a low filling rate under the same working conditions. On the basis of satisfying the dedusting efficiency, the resonance chord dedusting system does not affect normal production and resistance is low. The spray pressure is controlled at 0.3–0.7 MPa and the optimal wind speed is 3–4 m/s. According to the theoretical calculation and experimental data, the optimal filling rate of a vibrating string grid plate is 77.8%, spray pressure is 0.7 MPa, and wind speed is 3.5 m/s. Dust removal with low resistance and improved economic benefit can thus be obtained.