Question

Two identical pulses whose centres are initially $16\text{cm}$ apart are moving towards each other on a stretched string with same speed as shown in the figure. After $4$ seconds, if the vertical displacement for resultant pulse is zero then the speed of pulses are

• A. $2\text{cm/s}$
• B. $1\text{cm/s}$
• C. $4\text{cm/s}$
• D. $8\text{cm/s}$

Answer 1

The correct option is A $2\text{cm/s}$

At $t=0$

The distance between centre of pulses is $16\text{cm}$
The velocity of any of the pulse with respect to another pulse is,
$v_{\text{rel}}=v+v=2v$
Since, the vertical displacement of resultant pulse at $t=4\text{s}$ becomes zero, it means string has become horizontal.

$t=4\text{s}$

$\Rightarrow$The relative displacement of centre of pulses is $16\text{cm}$
$\Rightarrow \Delta x=v_{\text{rel}}\times t$
$\Rightarrow 16=2v\times 4=8v$
$\therefore v=2\text{cm/s}$