A wave is described by y(x,t)= 0.1 sin(3x - 10t), where x is in meters, y is in centimeters and t is in seconds.How long does it take the wave to travel 2.0 m?
A)0.6 s
B)1.0 s
C)3.0 s
D)6.7 s
E)10 s

Question

Quizplus · Accepted Answer

The wave equation is given by $y(x,t) = 0.1 \sin(3x - 10t)$. The term inside the sine function, $3x - 10t$, represents the wave's phase, where $3$ is the wave number (k) and $-10$ is related to the angular frequency ($\omega$). The speed of the wave (v) can be determined by the relationship between the wave number and the angular frequency, given by $v = \frac{\omega}{k}$. Here, $\omega = 10$ and $k = 3$, so $v = \frac{10}{3} \, \text{m/s}$. To travel 2.0 m, the time (t) required is given by $t = \frac{\text{distance}}{\text{speed}} = \frac{2.0 \, \text{m}}{10/3 \, \text{m/s}} = 0.6 \, \text{s}$.

A Wave Is Described by Y(x,t)= 0