Wave Mechanics Vibration Of String Question 48
A string is rigidly tied at two ends and its equation of vibration is given by $ y=\cos 2\pi t\sin (\sin \pi x). $ Then minimum length of string is
[RPMT 2001]
Options:
1 m
B) $ \frac{1}{2}m $
5 m
2pm
Show Answer
Answer:
Correct Answer: B
Solution:
$ y=\sin 2\pi x\cos 2\pi t $ , comparing it with standard equation $ y=2A\sin \frac{2\pi x}{\lambda }\cos \frac{2\pi t}{T} $ We have $ \frac{2\pi x}{\lambda }=2\pi x $
Therefore $ \lambda =1m $ Minimum distance of string (first mode) $ {L _{\min }}=\frac{\lambda }{2}=\frac{1}{2}m $
BETA
