A standing wave is represented by $y = a \sin (100t) \cos (0.01x)$ where, $t$ is in second and $x$ is in…

A standing wave is represented by $y = a \sin (100t) \cos (0.01x)$ where, $t$ is in second and $x$ is in metre. Then, the velocity of the constituent wave is
  1. $10^2 \text{ ms}^{-1}$
  2. $10 \text{ ms}^{-1}$
  3. $1 \text{ ms}^{-1}$
  4. $10^4 \text{ ms}^{-1}$

Solution

Velocity of wave, $v = \frac{\omega}{k} = \frac{100}{0.01} = 10^4\text{ ms}^{-1}$

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