One end of a taut string of length 3 m along the -axis is fixed at

PHYSICS · Single correct · CBSE · Physics · Waves · Waves

Problem

One end of a taut string of length 3 m along the

x

-axis is fixed at

x = 0

. The speed of the waves in the string is

100 \text{ ms}^{-1}

. The other 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 waves is(are) [Adv. 2014] (1)

y(t) = A \sin \frac{\pi x}{6} \cos \frac{50\pi t}{3}

(2)

y(t) = A \sin \frac{\pi x}{3} \cos \frac{100\pi t}{3}

(3)

y(t) = A \sin \frac{5\pi x}{6} \cos \frac{250\pi t}{3}

(4)

y(t) = A \sin \frac{5\pi x}{2} \cos 250\pi t