Klimparskaya, OksanaSN # 14Experiment #14Standing Waves on a StringKlimparskaya, OksanaPartner’s name: Mordechai HershkopExperiment Date: 5/13/2019Due Date: 5/_ _ /2019_____________________________________________________________________________________IntroductionPurposea. To investigate resonance conditions for a vibrating string.b. To study dependence of wavelength on the tension and linear mass density of the string.TheoryIn any wave motion, wavelength () and frequency (f) of the wave is related by where v is the velocity of the propagation of the wave. The velocity, v of a wave ona stretched string depends on the tension, T, in the string and the mass per unit of the string , T, and is given byIf a stretched and vibrating string is clamped at both ends, like a guitar string, the wave reflects from the fixed ends and waves travel in both directions. The incident and reflected waves will combine according to superposition principle. When a proper amount of tension is applied along the string for a given length of the string,the waves travelling in opposite directions resonate and form a standing wave. Figure 1 shows two of the many possible modes of making standing waves on a 1| Page

Klimparskaya, OksanaSN # 14string. In the figures, N indicates the locations the string is stationary, called nodes,and A indicates the locations the string is vibrating with maximum amplitude, called antinodes. Standing waves are discrete phenomena, meaning that they only occur at specific values of wavelength. The distance from a node to an adjacent node (or from an antinode to adjacent antinode) is half of the wavelength. In order to form a standing wave a resonance condition has to be satisfied: where L L is the length of the string and n is an integer. For the standing wave in Figure 1a, the value of n is 1, and the wave pattern is called the fundamental or first harmonic. For Figure 1b, the value of n is 3, and the wave pattern is called the

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