Question

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 $100 \,ms ^{-1}$. 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)

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

Answer 1

Answer: (D)

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

Answer 2

Taking $y ( t )= A f ( x ) g ( t )$ & Applying the conditions:
1 ; here $x =3 \,m$ is antinode $\&\, x =0$ is node
2 ; possible frequencies are odd multiple of fundamental frequency.
where, $v_{\text {fiudamental }}=\frac{v}{4 \ell}=\frac{25}{3} Hz$