question_answer

A string is clamped at both the ends and it is vibrating in its 4th harmonic. The equation of the stationary wave is \[Y=0.3\sin \]\[(0.157x)cos\]\[(200\pi t)\]. The length of the string is : (All quantities are in SI units.)             [JEE Main 9-4-2019 Morning]

A) 20 m               

B) 80 m

C) 60 m               

D) 40 m

Correct Answer: B

Solution :

4th harmonic \[4\frac{\lambda }{2}=\ell \]                                      \[2\lambda =\ell \] From equation\[\frac{2\pi }{\lambda }=0.157\] \[\lambda =40\] \[\ell =2\lambda \] \[=80m\] Option [b]