Question

Two identical pulses in a stretched string whose centres are initially $8\text{cm}$ apart, are moving towards each other as shown in the figure. The speed of each pulse is $2\text{cm/s}$. After $2\text{s}$, the total energy of the pulse will be

• A. Zero
• B. Purely kinetic
• C. Purely potential
• D. Partly kinetic and partly potential

Answer 1

The correct option is B Purely kinetic

At $t=0$, both identical pulses are moving towards each other,


Relative speed of each pushe $=|\overrightarrow{v_1}-\overrightarrow{v_2}|$
$=|2-(-2)|=4\text{cm/s}$
After , t = 2 s, Relative distance covered $=4\times 2=8\text{cm}$ ( = distance between them)
Thus, these two pulses will superimpose.
Net amplitude, $A=A_1+A_2$
$\Rightarrow A=a+(-a)=0$ [Assuming amplitude each pulse to be a]
So, at $t=2\text{s}$, string will looks like,


As string is in normal condition (there is no distortion ), thus potential energy is zero.
From law of conservation of mechancial energy, all the energy is now in the form of kinetic energy.
Therefore, the total energy of the pulses will be purely kinetic at $t=2\text{s}$.