Wave motionHardBloom L3

Question

A transverse wave is propagating along +x direction. At t=2 sec, the particle at x=4m is at

y=2 mm.With the passage of time its y coordinate increases and reaches to a maximum of 4 mm. The wave equation may be (using ω and k with their usual meanings)

Options

A.$y = 4\sin(\omega(t + 2) + k(x - 2) + \frac{\pi}{6})$
B.$y = 4\sin(\omega(t + 2) + k(x) + \frac{\pi}{6})$
C.$y = 4\sin(\omega(t - 2) - k(x - 4) + \frac{5\pi}{6})$
D.$y = 4\sin(\omega(t - 2) - k(x - 4) + \frac{\pi}{6})$

Solution

Sol. The photo of string at t = 2 sec will look like :

So, Equation of graph ⇒ y = A sin $\left\lbrack k(x - 4) + \pi - \frac{\pi}{6} \right\rbrack$

wave equation ⇒ y = A sin $\left\lbrack k(x - 4) - \omega(t - 2) + \pi - \frac{\pi}{6} \right\rbrack$

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