Question

A travelling wave on a string is given by $y=A$ $A\sin [\alpha x+\beta t+\frac{\pi }{6}]$ The displacement and velocity of oscillation of a point $\alpha =$ $0.56/cm,\beta =12/sec$ $A=7.5cm,x=1$ $cm$ and $t=1s$ is

• A. $4.6cm,46.5cm{s}^{-1}$
• B. $3.75cm,77.94cm{s}^{-1}$
• C. $1.76cm,7.5{cms}^{-1}$
• D. $7.5cm,75cm{s}^{-1}$

Answer 1

The correct option is B $3.75cm,77.94cm{s}^{-1}$

$\begin{array}{c}y=7.5\sin \left[0.56\alpha +12t+\frac{\pi }{6}\right]\\ atx=1\\ \&t=1\\ y=7.5\sin \left[0.56+12+\frac{\pi }{6}\right]\\ =7.5\sin \left[12.56+\frac{\pi }{6}\right]\\ =7.5\sin \left[4\pi +\frac{\pi }{6}\right]\\ =3.75cm\end{array}$

$\therefore$ Option $B$ is correct .