The displacement of a travelling wave is represented by $y=A \cos(\alpha t - \beta x)$ where $t$ is

Question

The displacement of a travelling wave is represented by $y=A \cos(\alpha t - \beta x)$ where $t$ is time, $x$ is distance and $\alpha, \beta$ are constants in S.I. units. Then the wave velocity is

Professor PC Thomas Classes · Answer

(a) : The standard equation of a travelling wave is $y = A \cos(\omega t - kx)$. Comparing the given equation $y = A \cos(\alpha t - \beta x)$ with the standard equation, we get angular frequency $\omega = \alpha$ and angular wave number $k = \beta$. The wave velocity is given by $v = \frac{\omega}{k}$. Substituting the values, we get $v = \frac{\alpha}{\beta}$.