A wave of amplitude $A = 0.2\text{ m}$, velocity $v = 360\text{ ms}^{-1}$ and wavelength $60\text{ m}$ is…

A wave of amplitude $A = 0.2\text{ m}$, velocity $v = 360\text{ ms}^{-1}$ and wavelength $60\text{ m}$ is travelling along positive $X$-axis, then the correct expression for the wave is
  1. $y = 0.2\sin 2\pi \left( 6t + \frac{x}{60} \right)$
  2. $y = 0.2\sin \pi \left( 6t + \frac{x}{60} \right)$
  3. $y = 0.2\sin 2\pi \left( 6t - \frac{x}{60} \right)$
  4. $y = 0.2\sin \pi \left( 6t - \frac{x}{60} \right)$

Solution

$k = \frac{2\pi}{\lambda} = \frac{2\pi}{60}$ and $\omega = vk = (360)\left(\frac{2\pi}{60}\right) = 12\pi$ $\therefore y = 0.2 \sin 2\pi\left(6t - \frac{x}{60}\right)$

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