A) \[\lambda =\frac{\pi {{x}_{o}}}{4}\]
B) \[\lambda =2\pi {{x}_{o}}\]
C) \[\lambda =\frac{\pi {{x}_{o}}}{2}\]
D) \[\lambda =4\pi {{x}_{o}}\]
Correct Answer: C
Solution :
\[\operatorname{x}={{x}_{o}} Sin 2\pi \left[ nt-\frac{\operatorname{x}}{\lambda } \right]\] \[\operatorname{velocity} of wave = n\lambda \] \[\operatorname{Particle} velocity = \frac{dy}{dt}= 2\pi {{x}_{o}}n Cos 2\pi \left[ nt-\frac{\operatorname{x}}{\lambda } \right]\] \[{{\operatorname{V}}_{max}}~of\,\,Partlcle = 2\pi n{{X}_{o}}\] \[{{\operatorname{V}}_{p}} =4{{V}_{w}}\] \[2\pi n{{x}_{o}}=n\lambda \] \[\lambda =\frac{\pi {{\operatorname{x}}_{o}}}{2}\]
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