A transverse wave is described by the equation $y=0.05\sin (2x-4t)$, where $x$ and $y$ are in meters and $t$ is in seconds. What is the wave speed $v$?

Solution

1. The standard form of a transverse wave equation is $y=A\sin (kx-\omega t)$, where $k$ is the wave number and $\omega$ is the angular frequency.
2. By comparing $y=0.05\sin (2x-4t)$ to the standard form, we identify $k=2\text{ rad/m}$ and $\omega =4\text{ rad/s}$.
3. The wave speed $v$ is calculated using the formula $v=\frac{\omega }{k}$.
4. Substituting the values gives $$\begin{array}{rl}v& =\frac{4}{2}\\ & =2\text{ m/s}\end{array}$$.
5. Hence the answer is (C).