Wave motionMediumBloom L3
Question
Here given graph shows the motion of particle at x $= \frac{\lambda}{2}$of a progressive wave. 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 cos (ωt – kx), y = A cos (ωt + kx)
B.y = A cos (ωt – kx), y = A cos (ωt + kx)
C.y = A sin (ωt – kx), y = A sin (ωt + kx)
D.y = A sin (kx – ωt), y = A sin (ωt + kx)
Solution
Sol. Equation of graph:
y = A sin ωt
In +ve x direction, equation:
y = A sin $\left\lbrack \omega t - k\left( x - \frac{\lambda}{2} \right) \right\rbrack$
= A sin (ωt – kx + π)
In –ve x direction, equation:
y = A sin $\left\lbrack \omega t + k\left( x - \frac{\lambda}{2} \right) \right\rbrack$ = A sin (ωt + kx – π)
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