Question

Length of a string $OP$ fixed at both ends is $3m$. Tension in the string is $0.64N$ and mass per unit length of the string is $0.01kg/m$. Set up a standing wave in the string $OP$ in such a way that distance between two consecutive nodes is $\frac{1}{2}m$. At $t=0$ velocity of each particle of the string is zero and particle at $x=\frac{1}{6}m$ has transverse displaced as $1cm$ in upward direction (that is $y=+1cm$). The possible equation of standing wave in the string is:

• A. $y=2\cos 2\pi x\cos 16\pi t$
• B. $y=(2\times {10}^{-2})\sin \pi x\sin 16\pi t$
• C. $y=2\cos 2\pi x\sin 16\pi t$
• D. None of these

Answer 1

The correct option is A $y=2\cos 2\pi x\cos 16\pi t$