A) \[\lambda =\frac{\pi a}{4}\]
B) \[\lambda =\frac{\pi a}{2}\]
C) \[\lambda =\pi a\]
D) \[\lambda =2\pi a\]
Correct Answer: B
Solution :
Equation of displacement of wave \[y=a\,\sin \,2\pi \,\left( nt-\frac{x}{\lambda } \right)\] Velocity of wave \[v=\frac{dy}{dt}=2\pi na\,\cos \,2\pi 0\left( 2nt-\frac{x}{\lambda } \right)\] Maximum velocity \[=2\pi na\] (maximum value of cos is 1) But maximum, velocity = 4v given Hence, \[2\pi na=4n\lambda \] \[\lambda =\frac{\pi a}{2}\]
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