A) \[\lambda =2\pi {{y}_{0}}\]
B) \[\lambda =\pi {{y}_{0}}\]
C) \[\lambda =\frac{\pi {{y}_{0}}}{4}\]
D) \[\lambda =\frac{\pi {{y}_{0}}}{2}\]
Correct Answer: D
Solution :
The given equation is: \[y={{y}_{0}}\,\sin \,2\pi \left( f\,t-\frac{x}{\lambda } \right)\] Wave velocity \[=f\lambda \], Particle velocity \[u=\frac{dy}{dt}={{y}_{0}}.\,2\pi f\,\cos 2\pi \left( ft-\frac{x}{\lambda } \right)\] \[u={{y}_{0}}2\pi f\] According to question \[{{y}_{0}}\,2\pi f=4f\lambda \] So, \[\lambda =\frac{\pi {{y}_{0}}}{2}\]
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