With respect to A, the progressive wave
A) B lags by \[\frac{\pi }{2}\] and C leads by \[\frac{\pi }{2}\]
B) B lags by \[\pi \] and C leads by \[\pi \]
C) B leads by \[\frac{\pi }{2}\] and C lags by \[\frac{\pi }{2}\]
D) B leads by \[\pi \]and C lags by \[\pi \]
Correct Answer: C
Solution :
Equations of waves A, B and C are respectively \[{{y}_{A}}=A\,\sin \omega t\] \[{{y}_{B}}=A\,\sin \left( \omega t+\frac{\pi }{2} \right)\] \[{{y}_{C}}=A\,\sin \left( \omega t-\frac{\pi }{2} \right)\] Therefore, w.r.t. A, the progressive wave B leads by \[\frac{\pi }{2}\] and C lags by \[\frac{\pi }{2}\] .
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