Question

Two identical triangular wave pulses whose centres are initially $4\text{cm}$ apart, have been shown in figure given below. The speed of each pulse is $1\text{cm/s}$. After $2\text{second}$, the shape of resultant wave-pulse will be

• A. Triangular
• B. Rectangular
• C. Straight line
• D. None of these.

Answer 1

The correct option is C Straight line

$\Rightarrow$considering $t=0$ for the initial shape of pulses on the string.
After $t=2\text{s}$, the displacement of centre of one pulse w.r.t another pulse:
$\Delta x=(v_1+v_2)t=2\times 2=4\text{cm}$
The figure given below represents the snapshot of wave-pulses on string at $t=2\text{s}$

The displacement of particles is equal but in opposite direction, corresponding to each wave pulse.
$\Rightarrow$Hence on superposition, it will result the zero displacement of particles on string from their mean position.
$\therefore$Shape of resultant pulse will be a straight line.