Wave velocity from equation – Rankers Physics

Waves and its Characteristics: Practice Problem & Solution

If equation of a wave is given by \(y = 4\sin(0.4\pi x + 4\pi t + \frac{\pi}{3})\) where \(x\) and \(y\) are in m and \(t\) is in second.. Then the magnitude of wave velocity is
2 m/s
8 m/s
10 m/s
5 m/s

Short Solution (Best for NEET):

To solve this problem, we apply the core principles of Waves and its Characteristics. Understanding the underlying formula is key to arriving at the correct answer below:

Wave velocity is given by \(v = \frac{\omega}{k}\). From the wave equation, \(\omega = 4\pi\) and \(k = 0.4\pi\), which gives \(v = \frac{4\pi}{0.4\pi} = 10\text{ m/s}\).

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