9702/Oct Nov/12/2017/Q22

When sound travels through air, the air particles vibrate. A graph of displacement against time for
a single air particle is shown.

Which graph best shows how the kinetic energy of the air particle varies with time?

Solution:

Answer: D

Kinetic energy = ½ mv²

A graph of displacement against time for a single air particle is shown.  The gradient of the displacement-time graph gives the velocity of the air particle at that point in time. This is done by calculating the gradient of the tangent at that point.

The gradient (and hence, velocity) is found to be zero at the maximum displacement (the tangent is horizontal) and maximum when the displacement is zero (the tangent is steepest).

Thus, at time = 0, T and 2T the velocity is zero and hence kinetic energy is zero. [A and C incorrect]

But, between time = 0 and T or between time = T and 2T the displacement is zero (in case) twice. So, the velocity (and kinetic energy) reaches its maximum value 2 times in each of the 2 intervals.[B is incorrect]

Reference: PYQ - Oct/Nov 2017 Paper 12 Q22