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Sample Notes On Waves

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Published in: Physics
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The notes will help students to understand the Formation of stationary waves in a stretched string.

Fatima J / Hyderabad

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Qualification: M.Sc (vbs purvanchal university - 2017)

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  1. Formation Of Stationary Waves In Stretched String: 1. Stationary waves are formed by the superposition of two waves of same amplitude and frequency travelling in opposite direction in the same straight line. 2. A string is fixed between two rigid supports and excited perpendicular to its length to generate transverse waves which travel in opposite direction. 3. These waves get reflected and overlap to form stationary waves. Theory: = displacement due to incident wave Y2 = displacement due to reflected wave Y = Yl+Y2 = asin(kx ot) + asin(kx + ot) = 2asinkxcos ot At x = 0, 1/2, - -- ------------ nodes are formed At x = 1/4, 31/4 — — — - -------------- antinodes are formed Fundamental Frequency: Consider a string of length 'l' stretched between two rigid supports P and Q. V = velocity of the wave 1 = wavelength of the stationary wave T = tension in the string m = linear density of the string n = fundamental frequency From fig, I = 1/2 = 21 We know that, 21 m I Law: The fundamental frequency of a vibrating string is inversely proportional to the length of the string when tension and linear density are constant. 1 nl = constant Il Law: The fundamental frequency of a vibrating string is directly proportional to the square root of the tension when the length of the string and linear density are constant. nx/fr = constant Ill Law: The fundamental frequency of a vibrating string is inversely proportional to the square root of linear density when the length of the string and tension are kept constant 1 nvfi = constant

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