Question

Consider two waves passing through the same string. Principle of superposition for displacement says that the net displacement of a particle on the string is sum of the displacements produced by the two waves individually. Suppose we state similar principles for the net velocity of the particle and the net kinetic energy of the particle. Such a principle will be valid for

• A. Both the velocity and the kinetic energy
• B. The velocity but not for the kinetic energy
• C. The kinetic energy but not for the velocity
• D. Neither the velocity nor the kinetic energy.

Answer 1

The correct option is B

The velocity but not for the kinetic energy

According to principle of super position

${\overrightarrow{y}}_{net}=\overrightarrow{y_1}+\overrightarrow{y_2}$

Here $y_1\&y_2$ are particle displacement vectors

differentiating with respect to time.

$\frac{d{\overrightarrow{y}}_{net}}{dt}=\frac{d\overrightarrow{y_1}}{dt}+\frac{d\overrightarrow{y_2}}{dt}$

${\overrightarrow{v}}_{net}={\overrightarrow{v}}_1+{\overrightarrow{v}}_2$

Here velocities are vectors.

So yes the superposition law is applicable to velocities.

Now let us square both sides

$(v_{net}{)}^2=({\overrightarrow{v}}_1+{\overrightarrow{v}}_2{)}^2$

$v_{net}^2={v_1}^2+{v_2}^2+2v_1{v}_2$ (all are magnitudes)

So clearly the law of super position is not applicable for net kinetic energy.