A) \[\frac{\lambda }{4\pi }\]
B) \[\frac{2\lambda }{\pi }\]
C) \[\frac{\lambda }{2\pi }\]
D) \[\lambda \]
Correct Answer: A
Solution :
For a wave \[y=a\sin \frac{2\pi }{\lambda }(vt-x)\] Differentiating Eq. (i) w.r.t, t we get \[\frac{dy}{dt}=\frac{2\pi va}{\lambda }\cos \frac{2\pi }{\lambda }(vt-x)\] Now, maximum velocity is obtained when \[\cos \frac{2\pi }{\lambda }(vt-x)=1\] \[\Rightarrow \] \[{{v}_{\max }}={{\left( \frac{dy}{dt} \right)}_{\max }}=\frac{2\pi va}{\lambda }\] \[\Rightarrow \] \[{{v}_{\max }}=\frac{v}{2}\] \[\Rightarrow \] \[\frac{V}{2}=\frac{2\pi va}{\lambda }\] \[\Rightarrow \] \[a=\frac{\lambda }{4\pi }\]
You need to login to perform this action.
You will be redirected in
3 sec
