If the speed of the wave shown in the figure is $330\text{ ms}^{-1}$ in the given medium, then the equation…

If the speed of the wave shown in the figure is $330\text{ ms}^{-1}$ in the given medium, then the equation of the wave propagating in the positive $x$-direction will be (all quantities are in MKS units) A wave profile with amplitude 0.05 m and two full wavelengths spanning a total length of 0.25 m along the X-axis.
  1. $y = 0.05\sin 2\pi (4000t - 12.5x)$
  2. $y = 0.05\sin 2\pi (4000t - 122.5x)$
  3. $y = 0.05\sin 2\pi (3300t - 10x)$
  4. $y = 0.05\sin 2\pi (3300x - 10t)$

Solution

Here, $A = 0.05\text{ m}$, $\frac{5\lambda}{2} = 0.25 \Rightarrow \lambda = 0.1\text{ m}$ Now, standard equation of wave, $y = A\sin \frac{2\pi}{\lambda} (vt - x)$ Putting the given values, we get $y = 0.05\sin 2\pi (3300t - 10x)$

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