A) \[\lambda =2\pi \,A\]
B) \[\lambda =\frac{1}{2}\pi A\]
C) \[\lambda =\pi A\]
D) \[\lambda =\frac{1}{4}\pi A\]
Correct Answer: B
Solution :
The given equation of transverse wave is \[y=A\sin 2\pi \left( \frac{t}{T}-\frac{x}{\lambda } \right)\] Maximum particle velocity \[({{u}_{m}})=a\omega \] From standard wave equation,\[~a=A,\] \[\omega =2\pi n=2\pi \frac{v}{\lambda }\] \[\therefore \] \[{{u}_{m}}=A.2\pi \frac{v}{\lambda }=4v\] \[\Rightarrow \] \[\lambda =\frac{\pi A}{2}\]
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