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Statement of a problem № 3467

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A string vibrates according to the equation y = 4 sin 1/2 pi x cos 20pi t , where x and y are in centimetres and t is in seconds. (a) What are the amplitudes and velocity of the component waves whose superposition can give rise to this vibration? (b) What is the distance between the nodes? (c) What is the velocity of the particle in the transverse direction at x = 1.0 cm and when t = 9/4 s?

Solution:
A string vibrates according to the equation y  = 4 sin 1/2 pi x cos 20pi t , whe

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