Consider two waves passing through the same string. The principle...

According to the principle of superposition, the net displacement of a particle is given by $y = y_1 + y_2$.

The net velocity of the particle is the time derivative of the net displacement:

$v = \dfrac{dy}{dt} = \dfrac{d(y_1 + y_2)}{dt} = \dfrac{dy_1}{dt} + \dfrac{dy_2}{dt} = v_1 + v_2$

Thus, the principle of superposition is valid for the velocity.

The net kinetic energy of the particle is given by:

$K = \dfrac{1}{2}mv^2 = \dfrac{1}{2}m(v_1 + v_2)^2 = \dfrac{1}{2}m(v_1^2 + v_2^2 + 2v_1v_2)$

$K = K_1 + K_2 + mv_1v_2$

Since $K \neq K_1 + K_2$, the principle of superposition is not valid for the kinetic energy.

Therefore, the proposed principle remains valid for the velocity but not the kinetic energy.