Any point on a string carrying a sinusoidal wave is moving with its maximum speed when:
A)the magnitude of its acceleration is a maximum
B)the magnitude of its displacement is a maximum
C)the magnitude of its displacement is a minimum
D)the magnitude of its displacement is half the amplitude
E)the magnitude of its displacement is one fourth the amplitude

Question

Quizplus · Accepted Answer

The maximum speed of a point on a string carrying a sinusoidal wave occurs when the magnitude of its displacement is at a minimum. This is because the velocity of the point is proportional to the derivative of the displacement, which is itself a sinusoidal wave. The velocity is zero at the maximum and minimum points of the displacement, and is maximum at the zero points of the displacement. Therefore, the point on the string is moving with its maximum speed when the magnitude of its displacement is at a minimum.

Any Point on a String Carrying a Sinusoidal Wave Is