A longitudinal wave travels on a slinky or any long spring. The wave is represented by the equation x(x, t) = 2.1 cm cos(2000 rad/s t − 40 m⁻¹ x). What is the direction of motion of a point on the spring due to the wave? A) the ± y direction B) the ± z direction C) the ± x direction

Question

Quizplus · Accepted Answer

The equation shows that the displacement of a point on the spring, x(x,t), is a function of both time, t, and position along the spring, x. The terms within the cosine function represent the angular frequency, ω = 2000 rad/s, the time, t, the wave speed, v = ω/k = 2000 rad/s / 40 m⁻¹ = 50 m/s, and the spatial position, x. The fact that the wave equation involves both cos(ωt − kx) and x suggests that the wave is moving in the x-direction, in that an observer at any fixed point on the spring will observe the wave passing by him/her in what appears to be a motion in the positive or negative x-direction. Hence, the correct answer is C.

A Longitudinal Wave Travels on a Slinky or Any Long