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