1) One end of a taut string of length 3m along the x-axis is fixed at x=0. The speed of the waves in the string is 100ms-1. The order end of the string is vibrating in the y-direction so that stationary waves are set up in the string. The possible waveform (s) of these stationary wave is (are) A) $y(t)= A \sin\frac{\pi x}{6}\cos \frac{50\pi t}{3}$ B) $y(t)= A \sin\frac{\pi x}{3}\cos \frac{100\pi t}{3}$ C) $y(t)= A \sin\frac{5\pi x}{6}\cos \frac{250\pi t}{3}$ D) $y(t)= A \sin\frac{5\pi x}{6}\cos 250\pi t$ Answer: Option A,C,DExplanation: There should be a node at x=0 and antinode at x=3m Also, $v=\frac{\omega}{k}=100 m/s$ $\therefore$ y=0 at x=0 and $y=\pm A$ at x=3m Only (a).(c) and (d) satisfy condition.
