Explanation The expression for the displacement of the particle is, y ( x , t ) = A cos ( k x − ω t ) (1) Here, A is the amplitude of the wave. x is the position. k is the wave number. ω is the angular frequency. t is the time. The velocity of the particle is, v ( x , t ) = − A ω sin ( k x − ω t ) . (2) Refer to Figure (14-51): For point A : The displacement at point A is maximum. The condition for maximum displacement is, k x − ω t = 0 Substitute 0 for k x − ω t in equation (2). v ( x , t ) = − A ω sin ( 0 ) = 0 The velocity at point A is zero. Thus, the point A is (III) instantaneously at rest. For point B : The value of ω t < π so, substitute any value less than π in equation (1) y ( x , t ) = A cos ( k x − ω t ) The position of the particle is positive

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ISBN: 9780321976444

Author: James S. Walker

Publisher: PEARSON

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Equation of Waves

Wave is an oscillation or disturbance traveling in a medium. It performs the transportation of energy but does not carry any matter. This motion of waves will transport fuel in a medium without permanent transfer of mass (particle).

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Chapter 14, Problem 83GP

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Whether the points are moving upward, downward or instantaneously at rest.

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Whether the points are moving upward, downward or instantaneously at rest.

Solution Summary: The author explains how to determine whether the points are moving upward, downward, or instantaneously at rest.

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Whether the points are moving upward, downward or instantaneously at rest.

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