A) \[\lambda =2\pi \,{{y}_{0}}\]
B) \[\lambda =\pi \,{{y}_{0}}\]
C) \[\lambda =\frac{\pi \,{{y}_{0}}}{3}\]
D) \[\lambda =\frac{\pi \,{{y}_{0}}}{2}\]
Correct Answer: B
Solution :
\[Particle velocity\, =\,\,\,\frac{dy}{dt}\] \[\left( \frac{dy}{dt} \right)=\left( \frac{2\pi }{\lambda }v \right){{y}_{0}}\,\cos \,\frac{2\pi }{\lambda }(vt-x)\] \[{{\left( \frac{dy}{dt} \right)}_{\max }}\,\,=\,\,{{y}_{0}}\,\frac{2\pi \,v}{\lambda }\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(\because \,\,\cos \,\,\theta =1)\] Given, \[{{\left( \frac{dy}{dt} \right)}_{\max }}=\,\,2\,v\] \[{{y}_{0}}\frac{2\pi \,v}{\lambda }=2\,v\,\,\,\,\Rightarrow \,\,\,\,\lambda =\pi \,{{y}_{0}}\]
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