Wave motionHardBloom L3

Question

Here given snap shot at $t = \frac{T}{12}$ of a standing wave. Then the equations of the wave will be when particles are moving towards their extreme and when particles are moving towards the mean position respectively. $\left( Here,T = \frac{2\pi}{\omega} \right)$

Options

A.y = A sin kx sin ωt, y = A sin$\left( \omega t + \frac{2\pi}{3} \right)$ sin kx
B.y = A sin kx cos ωt, y = A sin$\left( \omega t + \frac{2\pi}{3} \right)$ sin kx
C.y = A cos kx cos ωt, y = A cos $\left( \omega t + \frac{2\pi}{3} \right)$sin kx
D.y = A cos kx sin ωt, y = A cos $\left( \omega t + \frac{2\pi}{3} \right)$cos kx

Solution

Sol. As per given shape, Equation of wave should be of the form (after shifting time)

y = A sin kx sin$\left\lbrack \omega\left\lbrack t - \frac{T}{12} \right\rbrack + \phi \right\rbrack$

For given time, ymax= $\frac{A}{2}$.

So, if going towards extreme ⇒ φ  = $\frac{\pi}{6}$

& if going towards mean ⇒ φ  = π – $\frac{\pi}{6}$

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