A transverse periodic wave is represented by the equation y(x, t) = 2.50 cm cos(2,500 rad/s t − 15.0 m−1 x). What is the direction of the velocity of the wave?
Question
A transverse periodic wave is represented by the equation y(x, t) = 2.50 cm cos(2,500 rad/s t − 15.0 m−1 x). What is the direction of the velocity of the wave?
Solution
The direction of the velocity of a wave is determined by the sign of the term involving both space (x) and time (t) in the wave equation. In the given equation, y(x, t) = 2.50 cm cos(2,500 rad/s t − 15.0 m−1 x), the term is -15.0 m−1 x. The negative sign indicates that the wave is moving in the positive x direction. Therefore, the velocity of the wave is directed in the positive x direction.
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