Question

At $t=0$, a transverse wave pulse travelling along positive $x-$direction with speed $3m/s$ in a string described by the function $y=\frac{9}{x^2}$ given that $x\ne 0$. Transverse velocity of particle at $x=3m$ and $t=3s$ will be

• A. $-\frac{1}{4}\frac{m}{s}$
• B. $\frac{1}{4}\frac{m}{s}$
• C. $-\frac{1}{8}\frac{m}{s}$
• D. $\frac{1}{2}\frac{m}{s}$

Answer 1

The correct option is A $-\frac{1}{4}\frac{m}{s}$

For general form of the wave, one has to replace $x$ by $(x-vt)$.
$y=\frac{9}{(x-3t{)}^2}$
The transverse velocity of the particle is $\frac{\delta y}{\delta t}$
$\frac{\delta y}{\delta t}=-\frac{18(-3)}{(x-3t{)}^3}$
$\frac{\delta y}{\delta t}=-\frac{18(-3)}{(3-9{)}^3}=-\frac{1}{4}m{s}^{-1}$