Wave motionHardBloom L3

Question

Here given snap shot of a progressive wave at $t = \frac{T}{6}$ with time period = T. Then the equation of the wave if wave is going in +ve x-direction and if wave is going in –ve x-direction will be respectively.$\left( Here,T = \frac{2\pi}{\omega} \right)$

Options

A.y = A sin $\left( kx - \omega t + \frac{\pi}{2} \right)$, y = A sin $\left( kx + \omega t - \frac{\pi}{6} \right)$
B.y = A cos (kx – ωt), y = A sin (kx + ωt)
C.y = A sin $\left( kx - \omega t - \frac{\pi}{6} \right)$, y = A sin $\left( kx + \omega t - \frac{\pi}{6} \right)$
D.y = A sin $\left( kx - \omega t + \frac{\pi}{2} \right)$, y = A sin$\left( kx + \omega t + \frac{\pi}{6} \right)$

Solution

Sol. Equation of graph: y = A sin$\left( kx + \frac{\pi}{6} \right)$

In +ve x direction

y = A sin $\left\lbrack kx - \omega\left( t - \frac{T}{6} \right) + \frac{\pi}{6} \right\rbrack$

= A sin $\left\lbrack kx - \omega t + \frac{\pi}{3} + \frac{\pi}{6} \right\rbrack$ = A sin $\left\lbrack kx - \omega t + \frac{\pi}{2} \right\rbrack$

In –ve x direction

y = A sin$\left\lbrack kx + \omega\left( t - \frac{T}{6} \right) + \frac{\pi}{6} \right\rbrack$

= A sin $\left\lbrack kx + \omega t - \frac{\pi}{3} + \frac{\pi}{6} \right\rbrack$

= A sin $\left\lbrack kx + \omega t - \frac{\pi}{6} \right\rbrack$

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