A) \[\lambda =\frac{\pi {{y}_{0}}}{4}\]
B) \[\lambda =\frac{\pi {{y}_{0}}}{2}\]
C) \[\lambda =\pi {{y}_{0}}\]
D) \[\lambda =2\pi {{y}_{0}}\]
E) \[\lambda =\frac{2\pi {{y}_{0}}}{3}\]
Correct Answer: B
Solution :
\[y={{y}_{0}}\sin 2\pi \left( ft-\frac{x}{\lambda } \right)\] ?? (i) For particle velocity, \[\frac{dy}{dt}=2\pi f{{y}_{0}}\cos 2\pi \left( ft-\frac{x}{\lambda } \right)\] Maximum particle velocity, \[{{\left( \frac{dy}{dt} \right)}_{\max }}=2\pi f{{y}_{0}}\] Wave velocity\[=f\lambda \] Accordingly, \[2\pi f{{y}_{0}}=4(f\lambda )\] Or \[\lambda =\frac{\pi {{y}_{0}}}{2}\]
You need to login to perform this action.
You will be redirected in
3 sec
