Solution:
For a standard wave equation \(y = A \sin(kx + \omega t + \phi)\), the wave velocity is \(v = \frac{\omega}{k}\). Here, \(k = 0.4\pi\) and \(\omega = 4\pi\), so \(v = \frac{4\pi}{0.4\pi} = 10\text{ m/s}\).
If equation of a wave is given by \(y = 4 \sin \left( 0.4\pi x + 4\pi t + \frac{\pi}{3} \right)\) where x and y are in m and t is in second. Then the magnitude of wave velocity is
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