Question

One end of a taut string of length $3m$ along the $x$ axis is fixed at $x=0$. The speed 8of the waves in the string is $100m{s}^{-1}$. 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)

• A. $y\left(t\right)=A\sin \frac{\pi }{6}\cos \frac{50\pi }{3}$
• B. $y\left(t\right)=A\sin \frac{\pi X}{3}\cos \frac{100\pi }{3}$
• C. $y\left(t\right)=A\sin \frac{5\pi X}{6}\cos \frac{250\pi }{3}$
• D. $y\left(t\right)=A\sin \frac{5\pi X}{6}\cos 250\pi t$

Answer 1

Answer: (A), (C), (D)

The correct options are
A $y\left(t\right)=A\sin \frac{\pi }{6}\cos \frac{50\pi }{3}$
C $y\left(t\right)=A\sin \frac{5\pi X}{6}\cos 250\pi t$
D $y\left(t\right)=A\sin \frac{5\pi X}{6}\cos \frac{250\pi }{3}$

$\text{Solution}:$

Clearly in the given situation a displacement node is present at x = 0 and a displacement antitode is present at x = 3m.

The velocity $v=\frac{\omega }{k}=100m{s}^{-1}$.

$\text{Hence A, C and D are the correct options}$