Find the speed of an ocean wave whose displacement is given by the equation $y = 3.7 \cos ( 2.2 x - 5.6 t )$ where x and y are in meters and t is in seconds.
A)2.5 m/s
B)1.9 m/s
C)3.5 m/s
D)4.5 m/s

Question

Quizplus · Accepted Answer

The speed of the wave can be determined by looking at the coefficient of the time variable $t$ in the wave equation. The general form of a wave equation is $y = A \cos(kx - \omega t)$, where $\omega$ is the angular frequency and relates to the wave speed $v$ through the equation $v = \omega / k$. In the given equation, $\omega = 5.6$ and $k = 2.2$, so the wave speed $v = 5.6 / 2.2 = 2.545$, which rounds to $2.5$ m/s.

Find the Speed of an Ocean Wave Whose Displacement Is y=3.7cos⁡(2.2x−5.6t)y = 3.7 \cos ( 2.2 x - 5.6 t )y=3.7cos(2.2x−5.6t)

Find the Speed of an Ocean Wave Whose Displacement Is $y = 3.7 \cos ( 2.2 x - 5.6 t )$