Q. A string is rigidly tied at two ends and its equation of vibration is given by $y = \cos{2\pi\ t\sin{2\pi x.}}$ Then minimum length of string is
A) $1\ m$
B) $\frac{1}{2}m$
C) $5\ m$
D) $2\ \pi m$
Explanation
(b) Given equation of stationary wave is
$y = \sin{2\pi x\cos{2\pi t,}}$ comparing it with standard equation
$y = 2A\sin\frac{2\pi x}{\lambda}\cos\frac{2\pi x}{\lambda}$
We have $\frac{2\pi x}{\lambda} = 2\pi x \Rightarrow \lambda = 1m$
Minimum distance of string (first mode) $L_{\min} = \frac{\lambda}{2} = \frac{1}{2}m$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.